Network aware source coding and communication 1st Edition Nima Sarshar

Network aware source coding and communication 1st
Edition Nima Sarshar download pdf
https://ebookfinal.com/download/network-aware-source-coding-and-
communication-1st-edition-nima-sarshar/
Visit ebookfinal.com today to download the complete set of
ebook or textbook!

Here are some recommended products that we believe you will be
interested in. You can click the link to download.
Practical Electrical Network Automation and Communication
Systems 1st Edition Cobus Strauss Cpeng Bsc (Eleceng)
Bcomm
https://ebookfinal.com/download/practical-electrical-network-
automation-and-communication-systems-1st-edition-cobus-strauss-cpeng-
bsc-eleceng-bcomm/
Digital Speech Coding for Low Bit Rate Communication
Systems Second Edition A. M. Kondoz(Auth.)
https://ebookfinal.com/download/digital-speech-coding-for-low-bit-
rate-communication-systems-second-edition-a-m-kondozauth/
Wireless Network Traffic and Quality of Service Support
Trends and Standards Premier Reference Source First
Edition Thomas Lagkas
https://ebookfinal.com/download/wireless-network-traffic-and-quality-
of-service-support-trends-and-standards-premier-reference-source-
first-edition-thomas-lagkas/
Provider s Coding Notes Billiing and Coding Pocket Guide
1st Edition Alice Ann Andress
https://ebookfinal.com/download/provider-s-coding-notes-billiing-and-
coding-pocket-guide-1st-edition-alice-ann-andress/

Adolescent Online Social Communication and Behavior
Relationship Formation on the Internet Premier Reference
Source 1st Edition Robert Zheng
https://ebookfinal.com/download/adolescent-online-social-
communication-and-behavior-relationship-formation-on-the-internet-
premier-reference-source-1st-edition-robert-zheng/
Enabling context aware web services methods architectures
and technologies 1st Edition Quan Z. Sheng
https://ebookfinal.com/download/enabling-context-aware-web-services-
methods-architectures-and-technologies-1st-edition-quan-z-sheng/
Handbook of Energy Aware and Green Computing Volume 2 1st
Edition Ishfaq Ahmad (Editor)
https://ebookfinal.com/download/handbook-of-energy-aware-and-green-
computing-volume-2-1st-edition-ishfaq-ahmad-editor/
Coding Notes Pocket Coach for Medical Coding 3rd Edition
Alice Anne Andress
https://ebookfinal.com/download/coding-notes-pocket-coach-for-medical-
coding-3rd-edition-alice-anne-andress/
Visual Media Coding and Transmission 1st Edition Ahmet
Kondoz
https://ebookfinal.com/download/visual-media-coding-and-
transmission-1st-edition-ahmet-kondoz/

Network aware source coding and communication 1st
Edition Nima Sarshar Digital Instant Download
Author(s): Nima Sarshar; et al
ISBN(s): 9780521888400, 0521888409
Edition: 1
File Details: PDF, 3.54 MB
Year: 2011
Language: english

Network-aware Source Coding and Communication
An introduction to the theory and techniques for achieving high-quality network com-
munication with the best possible bandwidth economy, this book focuses on network
information ﬂow with ﬁdelity. Covering both lossless and lossy source reconstruction,
it is illustrated throughout with real-world applications, including sensor networks and
multimedia communications. Practical algorithms are presented, developing novel tech-
niques for tackling design problems in joint network-source coding via collaborative
multiple-description coding, progressive coding, diversity routing, and network coding.
With systematic introductions to the basic theories of distributed source coding, net-
work coding, and multiple-description coding, this is an ideal self-contained resource
for researchers and students in information theory and network theory.
Nima Sarshar is an Associate Professor of Software Systems Engineering at the Uni-
versity of Regina, Canada. The recipient of best paper awards at IEEE P2P 2004 and
SPIE VCIP 2008, his research interests include network communication of multimedia
signals, large-scale distributed computing, and P2P computing.
Xiaolin Wu is a Professor in the Department of Electrical and Computer Engineering at
McMaster University, Canada. His research interests include multimedia signal process-
ing and communications, data compression, and visual computing. He is an IEEE Fellow
and currently serves as an Associate Editor of IEEE Transactions on Image Processing.
Jia Wang is an Associate Professor in the Department of Electrical Engineering at
Shanghai Jiao Tong University, China. His research interests include multi-user infor-
mation theory and its application in video coding.
Sorina Dumitrescu is an Associate Professor in the Department of Electrical and Com-
puter Engineering at McMaster University, Canada. Her research interests lie in robust
image coding, data compression for networks, multiple-description source codes, quan-
tization, and joint source-channel coding.

Network-aware Source Coding
and Communication
NIMA SARSHAR
University of Regina
XIAOLIN WU
McMaster University
JIA WANG
Shanghai Jiao Tong University
SORINA DUMITRESCU
McMaster University

CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town
Singapore, São Paulo, Delhi, Tokyo, Mexico City
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521888400
c
Cambridge University Press 2011
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 2011
Printed in the United Kingdom at the University Press, Cambridge
A catalog record for this publication is available from the British Library
Library of Congress Cataloging-in-Publication Data
Network-aware source coding and communication / Nima Sarshar . . . [et al.].
p. cm.
Includes bibliographical references and index.
ISBN 978-0-521-88840-0 (Hardback)
1. Telecommunication–Data processing. 2. Telecommunication–Trafﬁc. 3. Computer programming.
I. Sarshar, Nima. II. Title.
TK5102.5.N396 2011
005.1–dc23
2011014524
ISBN 978-0-521-88840-0 Hardback
Cambridge University Press has no responsibility for the persistence or
accuracy of URLs for external or third-party internet websites referred to
in this publication, and does not guarantee that any content on such
websites is, or will remain, accurate or appropriate.

Contents
1 Introduction page 1
1.1 Network representation of source coding problems 1
1.2 Source coding and communication in networks with more complex
topologies 3
1.3 Separability of source coding and on-route processing 4
1.3.1 Lossless communication of a single source 4
1.3.2 Single source communication to sinks with equal max-ﬂow 4
1.4 More general scenarios 4
1.4.1 Distributed source coding in arbitrary networks 4
1.4.2 Lossy communication of a single source in arbitrary networks 5
1.5 Applications and motivations 7
1.6 Network-aware source coding and communication: a formal deﬁnition 8
1.7 Organization of this book 9
Part I The lossless scenario 13
2 Lossless multicast with a single source 15
2.1 Network coding, the multicast scenario 15
2.2 Information multicast with routing only 16
3 Lossless multicast of multiple uncorrelated sources 20
3.1 Multi-unicast problem 20
3.2 Multi-unicast with routing and network coding on directed acyclic graphs 20
3.2.1 Coding gain in directed networks can be high 21
3.2.2 Cuts in undirected graphs 22
3.2.3 Coding gain in undirected networks: Li and Li’s conjecture 23
3.3 Concluding remarks 23
4 Lossless multicast of multiple correlated sources 25
4.1 Slepian-Wolf problem in simple networks 25
4.1.1 Main theorem and its proof 26
4.1.2 Slepian-Wolf coding for many sources 29
4.1.3 Slepian-Wolf code design 29

vi Contents
4.2 Slepian-Wolf problem in general networks 34
Part II The lossy scenario 37
5 Lossy source communication: an approach based on multiple-description codes 39
5.1 Separating source coding from network multicast 39
5.2 Beyond common information multicast: rainbow network flow 41
5.3 Multiple-description coding: a tool for NASCC 42
5.3.1 Example 5.1 43
5.3.2 Example 5.2 45
5.3.3 Design issues 47
5.4 Rainbow network flow problem 48
5.5 Code design 50
5.5.1 MDC using PET 50
5.5.2 Optimizing code for a fixed rainbow flow 52
5.5.3 Discrete optimization approaches 53
5.6 Numerical simulations 54
5.6.1 Network simulation setup 54
5.6.2 Effect of the number of descriptions 55
5.6.3 The effect of network size 55
5.6.4 The effect of the performance of path optimization algorithms 57
6 Solving the rainbow network flow problem 59
6.1 Complexity results of the CRNF problem 59
6.2 A binary integer program for CRNF on directed acyclic graphs 61
6.2.1 Formulation 61
6.2.2 The DAG requirement 62
6.3 Solving CRNF on tree-decomposable graphs 62
6.3.1 Calculation of the optimal flows 63
6.3.2 Flow coloring 65
6.4 Optimal CRNF for single sink 67
7 Continuous rainbow network flow: rainbow network flow with unbounded delay 71
7.1 Continuous rainbow network flow 71
7.2 Achievability results 72
8 Practical methods for MDC design 82
8.1 Overview of MDC techniques 82
8.2 Optimal design of multiple-description scalar quantizers (MDSQ) 84

Contents vii
8.2.1 MDSQ–deﬁnition and notations 84
8.2.2 Generalized Lloyd algorithm for optimal MDSQ design 87
8.2.3 Index assignment 88
8.3 Lattice MDVQ 91
8.3.1 Preliminaries 92
8.3.2 Distortion of MDLVQ 94
8.3.3 Optimal MDLVQ design 96
8.3.4 Index assignment algorithm 96
8.3.5 K-fraction sublattice 97
8.3.6 Greedy index assignment algorithm 98
8.3.7 Examples of greedy index assignment algorithm 99
8.3.8 Asymptotically optimal design of MDLVQ 101
8.3.9 Asymptotical optimality of the proposed index
assignment 101
8.3.10 Optimal design parameters ν, N, and K 102
8.3.11 Non-asymptotical optimality for K = 2 107
8.3.12 A non-asymptotical proof 107
8.3.13 Exact distortion formula for K = 2 108
8.4 S-similarity 111
8.5 Local adjustment algorithm 113
8.6 PET-based MDC 116
8.6.1 Exact solution for the general case 119
8.6.2 Fast matrix-search algorithm for convex case 121
8.7 General MDC based on progressive coding 125
8.7.1 Framework description 125
8.7.2 G-MDC rate optimization 127
8.7.3 G-MDC description construction 129
9 Using progressive codes for lossy source communication 132
9.1 Lossy source communication with network coding: an introduction 132
9.2 Formulation 134
9.3 Layered multicast with intra-layer network coding 135
9.3.1 Conditions for absolute optimality of LM with intra-layer
network coding 135
9.3.2 Optimization of layered multicast strategy 138
9.4 Layered multicast with inter-layer network coding 141
9.4.1 Flow optimization for inter-layer network coding 141
9.4.2 Network code construction 148
9.4.3 Performance evaluation 152
9.4.4 Conclusions 155
10 Lossy communication of multiple correlated sources 158
10.1 Simple Wyner-Ziv 158
10.2 The Wyner-Ziv theorem and its proof 159

viii Contents
10.2.1 Strong typicality and Markov lemma 159
10.2.2 Proof of the Wyner-Ziv theorem 160
10.3 Wyner-Ziv function for Gaussian sources and binary sources 162
10.3.1 Gaussian sources 162
10.3.2 Binary sources 162
10.4 Wyner-Ziv code design 163
10.5 Problems closely related to Wyner-Ziv coding 164
10.5.1 The (direct) multi-terminal source coding problem 164
10.5.2 The CEO problem (indirect multi-terminal source coding) 167
10.6 A summary of the network source coding problem of no more than two
encoders and decoders 168
References 171
Index 178

1 Introduction
To state intuitively, the question investigated in this book is the following:
How does one communicate one or more source signals over a network from nodes
(servers) that observe/supply the sources to a set of sink nodes (clients) to realize the
best possible reconstruction of the signals at the clients?
The above question sets the unifying theme for the problems studied in this book,
and, as will be made clear in this introduction, contains some of the most important and
fundamental problems in information and network communication theory.
1.1 Network representation of source coding problems
Let’s start with the observation that even the simplest source coding problems have
(perhaps trivial) network representations. Figure 1.1, for instance, shows network rep-
resentations of the three arguably most fundamental source coding problems. Here, the
goal is to communicate a single source signal X, from a single server node s to one
or more sinks. Each link of the network has a “capacity” assigned to it, which, when
properly normalized, indicates the number of bits that can be communicated over that
link, without errors, for every source symbol emitted from X.
Figure 1.1(a) is the simplest source coding problem. The receiver node t receives an
R1 bits encoding of X from the source node s. If X admits a rate-distortion function
DX (R), the reconstruction error at t is at best dt = DX (R1). Of course if X is deﬁned
on a ﬁnite alphabet, then for large enough R1, there is a possibility to communicate X
losslessly, or without distortion (i.e., dt = 0).
Figure 1.1(b), on the other hand, is the network representation of the progressive
source coding problem, when R1 R2, while Fig. 1.1(c) represents the network of two-
description multiple-description source coding problem. In the latter case, sink node t1
receives a description of X with rate R1, while t2 receives another description of rate
R2. Node t3 receives both descriptions, and in the terminology of multiple-description
coding (MDC), it acts as the joint decoder.
These examples correspond to the case of a single source signal X. Same is true for
problems involving multiple source signals observed by multiple, usually
non-communicating, encoders; problems often called distributed source coding. The
problem becomes particularly interesting when the multiple signals in question are cor-
related. Figure 1.1(a) is the simplest setting of a distributed source coding problem in

2 Introduction
which two correlated sources X and Y are encoded at two separate (non-communicating)
nodes s1 and s2, and are communicated to a single receiver node (or decoder), t.
This problem is called Slepian-Wolf distributed source coding [1] when the two
sources are on ﬁnite alphabets and the goal is lossless communication of both of them
to the sink t. Slepian and Wolf found necessary and sufﬁcient conditions on the rates
R1 and R2 for which lossless communication of both sources X and Y to t is feasi-
ble. In the special case where R2 = ∞, i.e., the source Y is losslessly present at the
decoder only, the problem of distributed source coding is usually called the Wyner-Ziv
problem [69].
There is a large body of literature on theoretical and practical aspects of source
coding problems with simple network representations as in Figs. 1.1 and 1.2. These
include the complete characterization of achievable rate-distortion regions for many
classes of important signals [2], [1] as well as powerful practical coding approaches that
s t1
R1
(a) Simple source coding
s t1 t2
(b) Progressive encoding
s t3
t1
t2
(c) Multiple-description coding
R1 R2
Figure 1.1 Network representation of fundamental source coding problems
s1
s2
t
R1
R2
Figure 1.2 The network representation of Slepian-Wolf, Wyner, and Wyner-Ziv problems

1.2 Source coding and communication in networks 3
perform close to these theoretical limits, some of which will be reviewed throughout
this book.
1.2 Source coding and communication in networks with more complex
topologies
For networks discussed so far, network structures are very simple. Since the communica-
tion links are assumed to be error-free, the network communication aspect of the source
coding-and-networking problem is trivial. In particular, once the source or sources are
encoded, the encodings are simply passed over the corresponding links. Recent advances
in network information ﬂow (e.g., network coding), however, suggest that there is much
more to network communication than simple information relay.
This book intends to not only cover some of the above mentioned special cases of
source coding in networks, but to go beyond, by exploring problems with networks
of complex topologies. Figure 1.3 shows the two simplest network information ﬂow
scenarios. In both scenarios, there is a single source to communicate from s to one or
more sink nodes, over an arbitrarily complex network. For these arbitrary networks,
as schematically depicted in Fig. 1.3, a new dimension enters the problem – that of
on-route information processing. As will become clear shortly, in most scenarios, source
coding is accompanied by network coding and routing (an aspect that we call on-
route processing) in a nontrivial fashion and, thus, in general, the two have to be
considered jointly. In other words, optimal utilization of network resources requires a
joint consideration of both source coding and on-route processing.
Figure 1.3 Unicast vs. multicast source communication

4 Introduction
1.3 Separability of source coding and on-route processing
Before getting to more general scenarios, we first review some of the few cases in which
source coding and on-route processing can in fact be separately performed without loss
of optimality.
1.3.1 Lossless communication of a single source
If X is defined on a finite alphabet, and the goal is a lossless communication of X from
s to all the sink nodes, then source coding and communication can be broken down into
two steps without loss of optimality, (1) a source coding step and, (2) a network com-
munication step. The network communication step, however, is fundamentally different
in the unicast and multicast scenarios.
Suppose the entropy of the source signal X is H(X). Then, in the unicast scenario, X
can be communicated to the single source node t losslessly if and only if the max-flow
from s to t is at least H(X). Furthermore, it suffices to perform only routing (in fact
simple relaying) in the network communication step. For the multicast scenario, on the
other hand, the source X can be communicated from s to sinks, if and only if the max-
flow from s to every sink node is at least H(X). Furthermore, network communication,
in general, requires re-encoding of information at relay nodes (i.e., network coding).
1.3.2 Single source communication to sinks with equal max-flow
Another special case in which source coding and network communication can be sepa-
rated without loss of optimality is when a single source X has to be communicated from
s to sink nodes with equal max-flow h. In that case, one can separately encode X to rate h
and then use network coding (in the multicast scenario) or simple routing (in the unicast
scenario) to communicate the source encoding to the sink nodes. If the source admits a
rate-distortion function DX (R), the distortion DX (h) is achievable at all sink nodes. It is
easy to verify that this is the smallest achievable distortion, given that the max-flow to
each sink node is h. These results are reviewed in more detail in Chapter 2.
1.4 More general scenarios
It turns out that source coding and network communication are non-separable in most
other scenarios, some important cases of which are reviewed next.
1.4.1 Distributed source coding in arbitrary networks
The Slepian-Wolf network settings in Fig. 1.2 can be generalized to the case of an
arbitrary network, as in Fig. 1.4. If X and Y are on finite alphabets, necessary and
sufficient conditions under which they can be losslessly communicated to the sink nodes
t1, t2, . . . , tn have been found recently [3].

1.4 More general scenarios 5
Figure 1.4 Slepian-Wolf coding in general networks
One important question discussed in [4] is whether distributed source coding can be
separated from network communication for Slepian-Wolf problem in arbitrary networks.
What happens if one encodes X to R1 bits, and multicasts it from s1 to all receivers and
then encodes Y into R2 bits and multicasts it to all sinks from s2? It turns out that
this separation strategy is suboptimal in general. More precisely, for many cases, it is
impossible to losslessly communicate X and Y to all the sinks unless distributed source
coding and network coding are done jointly. This warrants the study of a new class of
codes, which can be called joint network source codes (JNSC).
1.4.2 Lossy communication of a single source in arbitrary networks
As we saw earlier, when there is only a single sink, or when the max-flow to all sink
nodes is the same, source coding and on-route processing can be separated without loss
of optimality.
However, the nature of the problem changes drastically when the set of sink nodes
has heterogeneous flow properties (i.e., they don’t have equal max-flows). In this case,
a joint consideration of source coding and on-route processing is necessary even when
only a single source is transmitted in the network. The scenarios in Fig. 1.5 illustrate how
source coding and on-route processing (here in particular network coding) can become
entangled in a complex way, as explained below.
Figure 1.5(a) illustrates the case where the source X has to be communicated only to
the nodes 5, 6. The max-flow into both nodes 5 and 6 is 2. Thus, as stated before, one
can optimally encode X into a source code stream of rate 2, break the stream into two
sub streams a and b, each of rate 1, and communicate them to nodes 5 and 6. Note that
network coding (i.e., bitwise XOR operation on streams a and b) is necessary at node 3.
Methods and results in network coding are briefly reviewed in Part I of this book.

6 Introduction
S
S
5
1
1
3
3
2
2
4
4
6
`
`
`
`
`
` `
`
`
a b
a b
a b
a≈b
a≈b a≈b
(a)
S
S
5
1
3
3
2
2
4
4
6
`
`
`
`
` `
`
a b
a b
a b
a≈b
a≈b a≈b
(b)
S
S
5
1
3
3
2
4
4
6
`
`
`
`
` `
`
`
a b
a b
a b
a≈b
a≈b a≈b
(c)
S
S
5
1
3
3
2
4
4
6
`
`
`
`
` `
`
`
a b
a b
a b
a≈b
a≈b a≈b
(d)
Figure 1.5 The Butterfly network for which all links have capacity one: When the sink nodes are,
(a) 5 and 6, (b) 1, 5, and 6, (c) 1, 2, 5, and 6, (d) 4, 5, and 6
But, what if nodes 1, 5, and 6 constitute the set of sink nodes, as in Fig. 1.5(b)? In
this case, the max-flow is 1 for node 1 and is 2 for nodes 5 and 6. The optimal strategy
is now to progressively encode X into a stream of rate 2. Take the first portion of this
stream to make another stream a of rate 1 and make the rest of the stream into another
stream named b, again of rate 1. Network coding should be used to get both a and b to
nodes 5 and 6 and stream a to node 1. Note that node 2 gets the stream b only. Since
this is the second portion of a progressively encoded source code stream, node 2 will
not be able to reconstruct X at all (but this is OK, since node 2 is not a sink node). This
“layered” coding and communication strategy is reviewed in Chapter 9.
Figure 1.5(c) is yet another scenario, in which nodes 1, 2, 5, and 6 are sink nodes. In
this case, the most general strategy is to encode X into two multiple-description source
code streams each of rate 1 (name them streams a and b). Then use network coding
to communicate both a and b to nodes 5, 6. Node 1 will receive only the description
a and node 2 will only receive b. The use of multiple-description codes for efficient

1.5 Applications and motivations 7
source multicast is reviewed in Chapters 5 and 6, while practical methods for designing
multiple-description code streams are reviewed in Chapter 8.
As Fig. 1.5(a) to Fig. 1.5(c) suggest, sometimes, it is possible to break (without the
loss of optimality) the task of source coding and on-route processing into a proper
concatenation of well understood source coding operations (e.g., progressive coding
or MDC), followed by network communication techniques (e.g., network coding or
routing). This breakdown, however, cannot be done blindly. In other words, the choice
of source encoding and network communication strategies should be made jointly.
In most other cases, however, full, joint consideration of source coding and on-route
processing is required. When nodes 4, 5, and 6 are sinks, for instance, none of the above
strategies is necessarily optimal (Fig. 1.5(d)).
The above examples suggest that a separate, formal treatment of the problem of source
communication in networks is required. In this book, we will gather all these problems
under the same umbrella, that of Network-aware Source Coding and Communication
or NASCC. We will review a wide spectrum of new and old results related to different
instances of the NASCC problem.
1.5 Applications and motivations
Our model of networks adopted in this text, in many ways, is an abstraction of computer
networks, and is consistent with layered design of today’s network protocols. The
network is modeled as a graph of interconnected nodes that can communicate with rates
constrained to the capacity of network links, i.e., the topological structure of the network
is explicitly taken into account.
Our model is particularly relevant to the Internet at the router level and to overlay
Peer-to-Peer (P2P) networks. As such, the immediate and by far the largest application
domain of this research is real-time multimedia streaming over the Internet. But all the
results of this book are valid in any other application area in which a data source (e.g.,
a physical measurement) has to be relayed to one or more receivers over an underlying
network, an important instance of which is signal communication in sensor networks.
For the clarity and concreteness of the presentations, this book will limit its discussions
on applications to networked multimedia communications.
Real-time multimedia communication spans a wide range of applications, including
digital TV and radio broadcasts over the Internet (e.g., IP-TV [5]), video conferencing,
video on demand (VoD), distant education, telemedicine, voice over IP (VoIP), online
computer games, virtual whiteboards, security and surveillance modules, and many
others. Current estimates show that real-time multimedia trafﬁc generated by real-time
streaming and VoIP only, accounts for more than 21 percent of the overall Internet
trafﬁc in Europe [6], a share that is expected to increase dramatically with the advent
of IP-TV technologies. Multicast applications are arguably the most resource-intensive
multimedia applications on the web. Most radio stations as well as hundreds of TV
channels now stream their live programs on the web. In February 2006, 148 million
users listened to radio stations streamed through Shoutcast.com [7] alone.

8 Introduction
The NASCC problem studied in this book investigates optimal utilization of band-
width resources for multimedia multicast applications. On the theoretical side, the study
of the NASCC problem, we believe, can fundamentally change our view of signal com-
munication in networks, in much the same way as network coding (discussed in the next
chapter) has changed our view of network information flow in the past few years.
1.6 Network-aware source coding and communication: a formal definition
The network model considered in this book is similar to now standard models in network
information flow theory [8]. In particular, the model of a network is very close to one’s
intuition of a computer network: an interconnected set of nodes, each capable of pro-
cessing and making decisions, which can reliably communicate over their connections
provided that the capacities of all connection links are respected.
We are interested in designing a networked communication system to communicate a
source signal from a set of source nodes (servers) to a set of sink nodes (clients), so that
the source signal can be reconstructed with the best average quality at all the sink nodes.
Unlike most frameworks of network information flow, the reconstruction of the source
does not need to be perfect. In fact, for most real valued multimedia signals, perfect
reconstruction is not necessary or even possible (the digitization process is already lossy
in nature). Another major difference is that the quality of the source reconstruction
and the input data used for such reconstruction do not need to be the same for all the
sinks.
In the version of the problem discussed in this book, it is assumed that the source has
been compressed off-line and has been deployed at the server nodes in advance. Again,
this formulation is from a networked multimedia application point of view, where a
multimedia content (e.g., a video clip) is encoded off-line and is deposited at one or
more server nodes in the network before the communication starts. Such an assumption
is of course not necessary when there is only a single server node in the network, a case
that in fact includes some of the most interesting scenarios, such as live media streaming.
At the time of presentation, the content is streamed to one or more users. The commu-
nication capacity of the links limits the amount of information that can be communicated
from node to node and hence the quality of the reconstruction of the source signal at
the sink nodes. We call the problem of finding the strategy that maximizes the overall
quality of the signal reconstruction at sink nodes, Network-aware Source Coding and
Communication, and it is formally defined next.
Problem formulation:
Formally, the Network-aware Source Coding and Communication (NASCC) problem is
defined by the following elements:
• A directed graph GV, E with nodes set V and edge set E ⊂ V × V.
• A number of, possibly correlated, sources X1, X2, . . . , XK over some common
alphabet . Of particular interest is the case where = RN , for some N.

• A function R = E → R+ that assigns a capacity R(e) to each link e ∈ E. Bandwidths
are normalized with the source bandwidth; therefore, R(e) is expressed in units of bits
per source symbol.
• Si, Ti ⊆ V, for i = 1, 2, . . . , K that denote the set of server and sink nodes respectively
for source Xi. We let S = ∪i Si, T = ∪i Ti denote the set of all server and sink nodes.
The server nodes observe, encode, and communicate Xk in the network. Server nodes
are not able to directly communicate (or collaborate) in the encoding process.
Throughout, we assume each source X admits a rate-distortion function DX (·) under
some family of distortion measures. For the most part, we also assume the source X is
progressively refinable.
Nodes can communicate with neighbor nodes at a rate specified by the capacity of
the corresponding link. R(e), therefore, specifies that an average of R(e) bits can be
successfully communicated over link e per source symbol emitted from X.
The task is to communicate the source Xi from the server nodes in Si and reconstruct
Xi at the sink nodes in Ti. Throughout this book, | · | denotes the cardinality of a finite
set. Distortion vectors dk = (dt, t ∈ Tk) ∈ R|Tk| for K = 1, 2, . . . , K are said to be
simultaneously achievable if Xk can be reconstructed with an average distortion of dt at
sink node t ∈ Tk by using a coding scheme that respects the capacity constraints on the
links, i.e., the rate of information per source symbol communicated over e is no greater
than R(e).
Unlike classical point to point, or even multi-terminal information theory, it proves
extremely hard to completely characterize the most general class of possible codes.
Therefore, just as in [8], we need to leave the details of the code unspecified.
A number of considerations about the above formulation are due. For clarity, let’s
assume that there is only one source X, with one set of receivers T.
• A theoretically intriguing problem is how to characterize the set of all achievable
distortion vectors d ∈ R|T|. Note that this problem includes the usual lossless network
coding problem as its special case, if the source alphabet is finite.
• An equivalent problem, which is more relevant practically, is that of finding a coding
scheme to minimize a weighted average distortion d(p) =

t ptdt for a weight-
ing vector of Lagrangian multipliers p = (pt; t ∈ T). This formulation is mostly
considered in this book.
The remainder of this book is a systematic review of the known results and recent
developments in dealing with the NASCC problem according to the taxonomy presented
in the introduction.
1.7 Organization of this book
Finding the most general source coding-network communication strategy remains an
open problem, with little hope for a solution. Even some of its simplest special cases

10 Introduction
Figure 1.6 A taxonomy of source coding and communication problems in networks and their
relation to the chapters of this book
(e.g., n-description source encoding) are known to be notoriously hard problems. In
this book, however, we adopt a pragmatic approach. We investigate the solutions to this
problem that use well-understood source coding techniques (e.g., progressive encoding,
MDC, Slepian-Wolf, or Wyner-Ziv coding) along with optimized network communica-
tion strategies (e.g., optimized routing, relaying, or network coding), to come up with
strong and practical solutions.
Figure 1.6 is a taxonomy of NASCC problems and their relationship to the chapters
of this book. A brief description of the chapters is given below.
• Chapter 2: Part I of this book, which starts with Chapter 2, deals with lossless commu-
nication of sources in networks. Chapter 2 is concerned with the case with only one
source node. We will consider scenarios where network coding is and is not allowed.
There are several excellent tutorials and textbooks already available on network cod-
ing. As such, this chapter is intended to review recent results with an emphasis on
algorithmic and complexity perspectives of designing optimal information delivery
mechanisms.
• Chapters 3 and 4: In these chapters, we extend the discussions from Chapter 2 to the
case of multiple sources. We consider the cases where information sources are corre-
lated and uncorrelated, as well as unicast and multicast scenarios. Chapter 3 covers
the case of independent source signals. Results and algorithms when network coding
is and is not allowed are reviewed. Discussions will include Li and Li’s conjectures

(when network coding is allowed) and multi-commodity ﬂow problems (when net-
work coding is not allowed). Chapter 4 reviews known results for multiple correlated
sources. Our discussion covers the Slepian-Wolf problem and its generalization to
arbitrary networks and multicast scenarios.
• Chapter 5: This chapter is the start of the second part of the book and deals with the
problem of lossy source communication in networks. Since lossy reconstruction is
now allowed, the rate-distortion optimization framework enters the picture. We will
discuss and motivate the problem through examples, which help the reader appreciate
the fundamental difference between the lossy and lossless scenarios.
• Chapter 6: In this chapter, we will review the Rainbow Network Flow (RNF) problem
in detail. RNF is the problem of RD-optimal distribution of multiple-description
codes in arbitrary networks and serves as the building block of some of the practical
solutions to lossy NASCC.
• Chapter 7: In this chapter, we investigate the problem of optimization of multiple-
description code designs and their network delivery strategies. We will review a
powerful practical solution to lossy source delivery in networks using the tools devel-
oped in this chapter and Chapter 6.
• Chapter 8: Other powerful lossy source delivery strategies are reviewed in Chapter 8.
These include, in particular, layered multicast of progressive codes with network
coding.
• Chapters 9 and 10: Finally, the generalization of the methods in Chapters 6–8 to the
case of multiple source signals are investigated. In particular, we review Wyner-Ziv
problems and their generalizations to the case of arbitrary networks, as well as routing
with side information.

Random documents with unrelated
content Scribd suggests to you:

But the child caught at her skirts again, still sobbing; she had felt
her mother’s arms about her, and half the dread and fear of
desertion which had hung over her, half the talk of the nurses which
had frightened her, was swept away; she had a mother. “Oh,
mamma,” she sobbed, “take me with you—I won’t make any noise!”
Margaret bent and kissed her again, her strange, wild look almost
frightening poor Gerty who stood completely discomfited and at a
loss, her honest blue eyes full of tears. “There, there!” the mother
whispered, “I’m glad you love me, Estelle, I’m coming, coming soon.
Oh, Gerty, go home with her!” she added suddenly, “take her away—
I—I can’t bear it!”
Gerty obeyed with a pale face. She bent down and whispered to
Estelle, kissed and cajoled and threatened until the child let go her
mother’s skirt and began to cling to the girl whom she really knew
far more intimately, for the good-hearted little secretary had spent
many an hour in that gloomy, magnificent nursery. Gerty’s hands
shook but she held the child, told her about some lovely things she
was going to bring her, a doll, a fairy-book, a toy which ran about
the floor of its own accord.
In the midst of it Margaret turned and fled; she had not dared to go
to the little boy, although, quite unacquainted with his mother, he
was merely staring in a dull, infantile way, his finger in his mouth,
ready, no doubt, to raise a sympathetic wail if his sister’s grief
warranted a chorus.
The mother, whose rights in the children had been settled by the
courts at six months in the year if she desired it, went on blindly
along the sunny avenue which seemed now to mock her with its
gayety. She turned sharply away from a crowded circle into another
street, hardly conscious where she went, but bent upon escape,
oblivion, silence.
The child’s cry had touched her chilled and starving heart; she saw
her life revealed; she had thrust away the ties of nature, the

demands of natural love and duty in her mad pursuit of happiness;
she had lost all and gained nothing.
She put up a shaking hand and drew down her veil; her lips were
dry and parched, it was difficult to breathe, she had to relax her
pace. Another corner brought her to an abrupt and horrified pause.
She came face to face with Mrs. O’Neal at a moment when she felt
that she could least abide the sight of any one. But with the shock of
recognition her scattered senses recovered themselves, her nerves
vibrated again, she summoned back her will.
“Margaret!” exclaimed the old lady, pausing, with her skirts gathered
up and her foot on her carriage-step, just the shadow of surprised
restraint in her manner, the indefinable change that greets the
altered social scale; “I’m—I’m delighted to see you! And how are
you, my dear?”
“Well,” Margaret replied, with an odd little laugh, for her quick ear
had caught the note; “don’t I look so?”
The bird of paradise on Mrs. O’Neal’s hat trembled. “No,” she said
flatly, “you don’t; you need building up, you should go to the country
for awhile. I’m due at bridge now or I should make you get in and
drive with me.”
“Thank you, I couldn’t,” Margaret replied, with forced calm; “I wish
you luck at cards instead.”
Mrs. O’Neal glanced at her coachman, stiff and expressionless upon
the box, then she leaned over and put a gentle hand on the younger
woman’s arm. “My dear, I congratulate you,” she murmured, “you’re
lucky to be free; I was so shocked to read this morning that Mr.
White had married Lily Osborne yesterday.”
Margaret suppressed her start of surprise. “Has he?” she said, “I
forgot to read the paper, and Gerty misses everything except the
ninety-eight cent bargains.”
“Yesterday—in New York!” said Mrs. O’Neal tragically; “I hope you’ve
got the children.”

Margaret quietly withdrew her arm. “Thanks, yes,” she said; “I’m
afraid you’ll be late for your bridge.”
As she walked on, her heart sank. Lily Osborne—of course she had
known it would be so! But if anything happened to her and Mrs.
White died—poor Estelle!
The cry of the child pursued her. Until now she had thought only of
herself, of her own misery, but the touch, the voice of the little girl
had reached her very soul; after lying dormant and unknown all
those years it was awakening, awakening to a reality so dreadful
that it was appalled, without hope, desolate. And shame, the shame
of a woman’s heart swept over her and shook her being to its
depths. The humiliation which comes upon a woman when she
knows, by some overwhelming perception, that her love is not fully
returned; she felt as if she had stripped her soul naked and left it
lying in the dust at Fox’s feet.
She walked on; agony winged her feet and she could not be still;
she avoided the places which she knew, and turned down strange
streets and byways. She had no thought of time. It grew late, the
short winter day drew to its close; still she walked on. While her
strength endured she went on,—it seemed as if pursuing fate drove
her. She was not physically strong, yet she was walking beyond the
endurance of most women.
As the twilight gathered and the lights began to start up here and
there, she turned, with a dim realization of her unfamiliar
surroundings and her sudden complete exhaustion. It was St.
Thomas’ Day, four days to Christmas; she had no recognition of it,
but, looking up, her eye caught the lighted vestibule of a church,
and she saw some women going in to vespers; an impulse made her
follow them. The heavy doors swung easily inward, and conscious
only of the shelter, the chance for rest, a moment to collect her
thoughts, she passed in.

The service was nearly concluded, but she paid no heed to that;
moving quietly across the aisle and finding a dark corner, she sat
down wearily, and crossing her arms upon the back of the pew in
front of her hid her face upon them. Mere physical weariness had
brought a dull relief to the gnawing pain at her heart; it clouded her
brain too, as weariness sometimes does, and she found the horrible
vivid thoughts which had tormented her slipping softly away into a
haze of forgetfulness; her mind seemed a mere blur.
The soft organ tones swelling through the dim church harmonized
with her mood; she lost herself, lost the agony of those past hours,
and rested there, inert, helpless, without power to think. She was
scarcely conscious of what passed around her, her throbbing head
felt heavy on her slender arms, and she listened, in a vague way, to
the music, aware at last of a stillness, then the rustle and stir of
people settling themselves back in the long pews. She stirred herself,
turning her face upon her arms.
A voice penetrated the stillness, a voice with that vibrant quality of
youth and passionate self-confidence.
“‘The wages of sin is death!’”
Margaret started and raised her head. Her eyes, blinded by the
sudden light in the chancel, flickered a moment and she passed her
hand across them; at last she saw quite plainly a young strong face,
with a tense eager look, white against the dark finishings of the
pulpit; she caught the dazzling white of his surplice, the vivid scarlet
of the hood which showed on his shoulders.
“‘The wages of sin is death!’” He repeated it, giving out his text in a
voice which was resonant with feeling.
Margaret sat back in her corner, gazing at him with fixed, helpless
eyes, her very soul dazed under the force of revelation which was
coming to her swiftly, overwhelmingly. The revelation of her own life,
not of God. As yet she framed no thought of that awful Presence,
found no interpretation of the tumult in her own soul, but she knew,
at last, that she had sinned. Sinned against herself, her womanhood,

her honor, her self-respect, sinned against the man she had married,
against the children she had borne, and, at last—oh, God!—against
the man she loved.
The wages of sin is death.
She rose, rose with an effort of will for her knees shook under her,
and drawing herself together, summoning all her strength and her
pride to hide the agony which was devouring her heart, she drew
down her veil and slipped out unnoticed, silent, like a shadow. Once
at the door, beyond the ring of that terrible young voice, she paused
and steadied herself by laying her hand on a pillar of the portico.
It was now very dark; the electric lights at the corner only made the
space where she stood more shadowy and secure; the air was chill,
damp, penetrating, and she shivered. A horrible sense of
homelessness and misery swept over her; she had cast herself out
of a home, she had deserted her children for the love of a man who
—oh, God!—who loved her not. She who had dreamed of happiness,
lived for it, fought for it, sinned for it, who would have purchased it
at the cost of heaven itself, had found at last, not happiness but her
own soul.
The wages of sin is death!
She wrung her hands in silent agony; was there no escape? She had
no belief but, at last, she felt that the very devils believed and
trembled. Was not God pursuing her with vengeance? Who else?

V
AT last the tumult of passion subsided and Margaret, still leaning on
the pillar of the church portico, looked out with bewildered eyes.
Again an overwhelming weakness swept over her and wiped out
some of the vivid misery.
She must go home—home! The word brought a dull pang of
anguish, she had no right to a home, for she had broken up her own
and orphaned her children. She closed her eyes, trying to shut out
the thoughts which stormed back, at a word, to assault her poor
fagged brain again. Then the soft sweet notes of the recessional
came out to her and she knew that in a few moments the dispersing
congregation would find her there; summoning all her flagging
energies she stepped down into the street and turning westward
was suddenly apprised of the fact that she had been in the old
church so often visible from the windows of Allestree’s studio. The
discovery brought her a feeling of relief; she was near the studio and
she could go there and telephone for a cab to take her back to the
hotel. Losing herself in the shadows of the darkest side of the poorly
lighted street, she hurried toward the old building on the corner and
saw, with relief, the light still shining in Allestree’s window as well as
in the curiosity-shop below.
She crossed the street and trying the side door found the latch
down. In another moment she was toiling wearily up the old stairs,
clinging to the balustrade with an absolute need of its support.
To her surprise the studio was empty; she called to Allestree,
supposing him to be, perhaps, in his storeroom above, but there was
no answer and she sank down in the nearest chair, too weary and
helpless to frame her thoughts. An open fire was burning low on the
hearth, and a half smoked cigarette lay on the mantel edge. He had
evidently gone out for a moment and would soon return. Margaret
roused herself and looked about her with a wretched feeling of
strangeness and separation from her own life. She seemed suddenly

detached, a mere onlooker where once she had been the centre of
the stage. There had stood the portrait of her, and there the picture
of Rose; both were gone! She even noticed that the little tea-table
was pushed away, and divined Allestree’s secret feeling. She knew
every detail of the room, the tapestries, the worn Turkey rug,
Robert’s old cigarette-case. It was intolerable; she rose, and going to
the table, where the telephone stood, saw Allestree’s portfolio and
the pen and ink. She would leave a line to explain her visit before
she called a cab, and she opened the portfolio to look for a scrap of
paper; as she did so her eye fell on the page of a letter written in old
Mrs. Allestree’s clear hand; unconsciously she read the lines before
her:
“Margaret has broken up Fox’s happiness twice, once when she
broke her own engagement to him, and now in separating him from
Rose—”
She closed the book sharply, suddenly aware of what she did and
deeply shamed by it, but the thought of the personal dishonesty of
her heedless act was lost in the sharper pang of realization; she saw
at last the light in which her actions had appeared to others. She
stood still, her face frozen, and a cry sprang to her lips from the
depths of hidden passion, the cry of some mortally wounded wild
creature who faces death alone. She knew it, she did not need to be
told it, but others knew it too! It was the bitter drop in her cup of
gall; the wild anguish which swept away all other realities, even the
desire for life, amazed her. For one moment she hated Rose with all
the strength of her undisciplined soul, the next a great wave of
humiliation submerged her being. She turned, forgetting the
telephone, forgetting everything but a desire to escape the meeting
with Allestree, groped her way to the door like a blind woman and
went down stairs. At the foot she hesitated; a step in the street
made her fear to meet Robert at the door, and she turned and
plunged into the curiosity-shop. She found herself behind the chintz
curtain, in the place which evidently served as a living-room for
Daddy Lerwick, and she saw a table spread for supper, while the

scent of garlic streamed from a pot on the stove. Hurrying across
the room she lifted the curtain and entered the shop.
Daddy Lerwick was leaning on the counter talking to a young girl
and passing a necklace back and forth in his fat hands. At the sound
of Margaret’s step they both turned and looked at her in surprise, a
surprise which gave place on his part to servile courtesy. But
Margaret scarcely noticed him; instead she saw the pale, worn face
of the girl, the pinched misery of her look as she glanced at the
stones in Lerwick’s coarse fingers. Margaret’s eyes following hers,
lighted, too, on the jewels; it was a topaz necklace, the mate to the
bracelet which she had prized so long ago. The intuition of misery,
the sixth sense of the soul which—no longer atrophied with
selfishness—had suddenly awakened within her, divined the secret.
She read the suspended bargain in Lerwick’s eye, the hopeless
anguish in the girl’s. It was only an instant; the thought came to her
like the opening of a dungeon door on the glare of midday. Then she
drew back to avoid an encounter with two more customers who had
entered the shop and who began at once to ask the prices of the
objects in the windows. Lerwick went forward to answer them; the
girl leaned on the counter, hiding her face in her hands; a shiver of
misery passed over her and Margaret saw it. Moved by an impulse,
as inexplicable as it was unnatural, she touched the shabby sleeve.
“What is the matter?” she asked softly.
The young woman looked up startled, but only for an instant, the
next the dull misery of her look closed over her face like a mask,
though her lip trembled. “He’s offered me fifteen dollars,” she
faltered; “I—I suppose I’ll have to take it.”
Margaret quietly put out her hand. “Will you sell it to me?” she said;
“I will give more and you will not have to give your name.”
The girl’s cheek crimsoned; she hesitated and gathered the necklace
into her hands; the gesture was pathetic, it bespoke the actual pang
of parting with an old keepsake.

Margaret saw it. “Come, come with me,” she said and led her back
through the door to the studio entrance; she no longer feared to
meet Allestree; a new impulse stirred her heart.
Under the light there she opened her purse and hastily counted her
money, she had a little over a hundred dollars in small bills. Hurriedly
thrusting a dollar or two back into her pocketbook, she pressed the
remainder into her companion’s hands, saying at the same time:
“Keep your necklace, I do not want it; I only wished to help you save
it.”
The young stranger looked at her in dull amazement, stunned by the
incomprehensible sympathy and generosity when she had long since
ceased to look for either. She drew a long shuddering breath. “Oh, I
can’t take so much!” she gasped out, “you—you must keep the
necklace!”
Margaret regarded her sadly. “Child,” she replied, “I’m more unhappy
than you are; I do not want either the money or the necklace; keep
them both!”
“Do you really mean it?” the girl whispered, her eyes fastened on the
face opposite in absolute wonder and doubt; “you really mean to
give me all this—and you want nothing?”
Margaret smiled with stiff lips. “Nothing!”
The pinched, childlike features of the stranger quivered; it seemed
as if the frozen sensibilities were melting under this touch of
common humanity. Suddenly she burst into an agony of tears,
slipping down upon the stairs, her slender shabby figure racked with
sobs. “He heard me!” she cried, “there is a God!”
Margaret looked at her strangely. “Do you think so?” she asked
vaguely, with parched lips, “do you believe in God?”
“Yes,” the girl cried, clasping her hands, “I prayed—oh, God, how I
prayed! It seemed as if He didn’t hear me, no help came and I
couldn’t pay; I couldn’t pay, and they didn’t believe me any more
because I’d failed—you don’t know, you’ve never failed like that! I

thought God didn’t care, that He had forgotten—but now—” she rose
from her knees, her face still wet with tears but singularly changed,
“I shan’t have to do it!” she cried, “here’s enough to begin all over
again, I can go on, I’m saved! He heard! Don’t you believe it? Don’t
you see it must be so?” she persisted, unconsciously catching at
Margaret’s draperies and her thin toil-worn hand closing on their
richness.
“For you, yes,” the older woman replied slowly; “good heavens, I
never knew how much money meant before!” she murmured,
passing her hand over her eyes again, “and you think—God heard
you—God?”
“He sent you!” the girl cried, exultantly, wildly happy; “oh, yes, I’m
sure of it—oh, God bless you!”
A strange expression passed over Margaret’s face. She leaned back
against the wall, pressing her hand to her heart. Then, as the girl
still sobbed softly, she touched her shoulder. “Open the door,” she
said quietly, “I—I must go, can you help me? I’m a little dizzy.”
The young woman sprang to her and put out her arm eagerly. “Let
me help you; oh, I’d do anything for you!”
Margaret smiled, a wan little smile that made her haggard brilliant
face weirdly sad. “It is nothing. There, the air from the outside
makes me well again, this place is choking!”
The stranger walked with her to the corner, eager to help her, to call
a cab, to put her on the cars, but as Margaret’s faintness passed she
refused, putting aside her protests with firm dismissal. “No, no, I can
go home,” she said bravely; “good-bye, I’m glad I could help you.”
“Oh, let me go with you, let me do something!” the girl appealed to
her eagerly.
But Margaret dismissed her and they parted, the young stranger
hurrying away down a narrow by-street while her benefactress
walked slowly toward the nearest avenue. But she had gone only a
few steps when she turned and looked after the shabby figure,

which was only a short distance from her. A vivid recollection of that
cry that God had heard her prayer, the absolute conviction of it,
swept over the stricken woman, and moved by an impulse which she
did not pause to question, Margaret ran after the girl through the
gathering mist and overtook her, breathless. She turned with a
frightened look, full of dread, no doubt, that she must yet give up
the miraculously acquired wealth, and she started when Margaret
laid a thin, ungloved hand on her arm.
“I wanted to ask you,” she began,—and then changed the sentence
swiftly into a command,—“pray for me to-night! You believe there is
a God—perhaps He’ll hear you again!”
“Indeed I will!” the girl cried, bewildered; “oh, I wish—”
But the unfinished speech was lost; Margaret had turned and swiftly
disappeared again into the folds of the mist; like a shadow the girl
saw her vanishing into deeper shadows; something uncanny and
marvellous seemed to lurk in the very thought of her beautiful
haggard face, the wildness of her smile, and the young woman
hurried away, hugging her treasure close, almost persuaded that she
had talked face to face with a being from another world.

VI
AVOIDING the crowded thoroughfares, and no longer remembering
her physical weariness or that she had walked for hours without food
or drink, Margaret hurried on.
She had thought of death, and the means to attain it most swiftly
and easily, but as she passed the brilliantly lighted chemist’s window,
with its arch hung with bright red Christmas bells, she put away the
thought; it was too cheap and sensational and, after all, if there
really were a God could she take that swift, shuddering plunge
through the blackness of death to meet Him? The wages of sin is
death! It thundered in her ears, making God the avenging Deity of
the Old Testament, for how little do those who preach sometimes
divine the pictures which they frame of Him who was lifted up, as
Moses lifted up the serpent in the wilderness, that all men might be
saved!
A strange new light began to come into Margaret’s soul, and against
it her thoughts took on dark and sharply outlined forms like the
shadows thrown on a white screen by the stereopticon; she began
to understand. Happiness, after all, was a dream, an imagination, a
word; it came not from any visible cause, but lay hidden in every
man’s heart like hope imprisoned in Pandora’s box. The secret of it
came to her at last,—life moved in an orbit; the past held the future,
the future the past, the present was but the connecting link in the
inexorable circle, it could not be broken while memory existed, while
a reckoning was required. She could no more break the links with
her past than she could destroy her immortal soul.
In her heart a new, secret thought, born of the strange girl’s
gratitude, moved her out of herself. She remembered Mrs. Allestree’s
words, and her love for Fox suddenly purged itself of its passionate
agony, its jealousy, its pain. Like a woman in a dream she found her
way at last to the hotel and climbed the stairs. Her face bore too
terrible signs of anguish, and she shrank from the elevator and the

curious stare of the servants. It was the dinner hour and the
corridors were deserted. She went quietly to her own room and did
not ring for her maid. She noticed that her evening gown had been
put out and the fire tended. Gerty was not there, she would scarcely
be there before nine o’clock, and Margaret went to her desk and sat
down and began to write in feverish haste; if she delayed, if she
stopped to think she might never do it and she was determined. She
bent to her task, white lipped and haggard, writing page after page
to Rose Temple. She poured out her heart; in righting Fox she
scarcely thought of herself, except that she should never see him
again, that Rose must and should marry him! For abruptly the divine
impulse of self-immolation had been born in the midst of the tumult
of her soul; a woman’s heart, like a eucalyptus tree, trembles with
the remembrance of anguish and the eternal sacrifice of love.
As she finished it the clock struck and she looked up startled; it was
eight o’clock; she had been out more than four hours. She sealed
her letter, stamped it and rose. For a moment her strength failed her
and she stood irresolute, but she was unwilling to trust another
hand, and she opened the door and took Rose’s letter down to the
post herself, avoiding the elevator again. After she had dropped it in
the letter-box in the lower hall, she climbed the long flight wearily to
her room. The fearful energy of the last few hours dropped from her
like a cloak, the effort was too much and she felt an overpowering
weakness, a sinking sensation; she had had such moments before
and the doctor had furnished her with some restoratives with a grim
injunction to avoid tiring herself. A vision of his grave face flashed
across her now and warned her. With the sudden ineffable sinking
and yielding, which came over her like a cloud and seemed to drop
her slowly, softly into space, was born a keen desire to live; Estelle’s
voice pierced her memory like a knife; she seemed to hear that
plaintive cry—“Mamma, mamma, come home!”
She made one more supreme effort to reach the medicines and was,
indeed, but a few yards from the cabinet which held them when her
strength yielded to that awful dark cloud which seemed to be
pressing down upon her, pushing her lower and lower into the

depths of silence. She slipped like water to the floor, her head upon
her outstretched arms, a faint shudder ran through her; she was
dimly conscious of sinking down, down into a black, fathomless
abyss. Again Estelle’s voice quivered through the clouds and mists
and reached her heart; she tried to struggle back, up through vague
distances, to answer it, but the mists grew thicker; she heard it once
again, no more! The soft, ineffable clouds pressed closer, enfolded
her; she sank lower, floated off over the edge of space and lost even
thought itself.

VII
FOR three days Fox had been under an almost unbearable strain.
Before and after speaking to Margaret of their marriage he had
plunged in the same agonizing struggle with himself. What diabolical
power had been at work to ruin his life, to frustrate his ambitions?
The strong egotism of his nature was aroused in all its absorbing
passion. On every hand he saw disaster; he had builded well in all
respects but one; in that he had miserably failed, and behold the
inevitable result! Like Margaret herself, he saw clearly at last; if he
had kept away from her, if he had broken from the spell of her
fascination and remained out of reach, this would never have been;
he had no one to thank but himself. It is usually so; when we get
down to the fundamental principles we have ourselves to blame for
the fall of the Tower of Siloam.
As he faced the immediate prospect of marriage with another
woman, he realized the strength and hopelessness of his love for
Rose. To think of her even in the same moment with Margaret was
abhorrent to him; he did poor Margaret scant justice at such times,
and the vivid realities of her newspaper celebrity was a scourge to
his sensitive pride. For these things he must give up all, he must pay
the price. He who crossed his path when this mood was on him was
unfortunate,—Fox was not a man to spare. His cruel irony, his
poignant wit had never been more feared on the floor of the House
than they were in those few days before Christmas.
The day after his decisive interview with Margaret he was late at the
Capitol, lingering in his committee-room after the others had left. On
his way home he dined at the club and was detained there by some
out-of-town friends until nearly eleven o’clock. When he finally left
the building he started home on foot, and even stopped at a news-
stand to buy some papers and magazines. It was twelve o’clock
when he went up to his rooms, and he was startled as he walked
down the corridor to see his door open and the vestibule lighted.

Sandy came to meet him with the air a dog wears who knows that a
friend is waiting for his master.
Allestree was sitting by the table in the study, and as Fox entered he
rose with a sober face, “I’ve been waiting for you for an hour,” he
said; “I have bad news.”
Fox stopped abruptly, his thoughts leaping instantly to Rose. “Bad
news?” he repeated in a strange voice.
Allestree met his eye, perhaps read his thoughts. “Yes, the worst,”
he replied; “Margaret is dead.”
“Margaret?” Fox dropped the papers he held, on the table, and
looked at him, bewildered; “impossible!”
“I wish it were so,” Allestree said quietly, hurrying on with his
disagreeable task; “it seems that she was out to-day for a long time
alone; no one apparently knows much about it except the elevator
boy and he says she was away from the hotel four hours or more. As
nearly as we know she was on foot and in the streets most of that
time. I know she was in my studio while I was out;” he colored as
he spoke; he had found his mother’s letter on the floor and piecing
the facts together had divined much. “She came home alone, went
to her rooms and was found there later, unconscious, on the floor.”
“Good God, where was Gerty?” Fox exclaimed, with a gesture of
horror.
“Margaret had sent her to Mrs. White with Estelle; there was some
painful scene in the street with the child—” Allestree stopped an
instant and then meeting his cousin’s eye he hurried on—“when
Gerty finally got to the hotel and found her it was too late; the
doctors say that if help had been at hand she might have been
saved. As it was she never regained consciousness. Gerty
telephoned to my mother, but she will not be back until to-morrow
morning; when I got there Margaret was gone.”
Fox sank into a chair by the table, and propping his head on his
hands stared blankly at a sheet of paper before him. “Why was I not

told?” he demanded hoarsely.
“Gerty tried to get you, both at the Capitol and here, but we could
not find you.”
“I was at the club,” Fox exclaimed and then: “Merciful heaven,
Allestree, how terrible, how harrowing! How impossible to realize!”
Allestree looked at him thoughtfully. “Do you think so?” he said, “it
has seemed to me for more than a year that I saw death in her face;
she had, poor girl, a face of tragedy.”
Fox groaned, covering his own face with his hands. His anger
against her of a moment before smote him with horrible reproach.
Living, he had ceased to love her, dead, she seemed suddenly to fill
his life to the exclusion of all else; she came to him again in the
guise of her thoughtless, happy, inconsequent youth which had
forged the links between them. He rose and began to walk the floor,
his pale face distorted with passion. “My God!” he cried suddenly; “I
—Allestree, is it possible that she divined the truth? That she knew
me for what I was, a sham, a mockery, a whited sepulchre?”
Knowing him and the unhappy woman, whose love for him had
wrecked her life, Allestree knew too much to speak; he was silent.
The storm of his cousin’s passion rose and beat itself against the
inevitable refusal of death. Poor Margaret! a few hours ago she had
held the power to ruin his career, now she had slipped quietly away
from him into the great Silence; the mute appeal of her unhappy
love touched his very soul as it had never touched it in life; the
impossibility of laying the blame for life’s miseries on the dead came
to him with overwhelming force, and she, who a moment before had
been guilty, in his thoughts, of embarrassing his future and blighting
his life, became suddenly the victim of his vanity, his idle pleasure
seeking which she had mistaken for love. He remembered, with
sudden horror and self loathing, his coldness, his bitterness toward
her, and the manner in which she had received his proposal of
marriage. A swift electrifying realization of the scene tore away his
selfish absorption; his manner of asking her had been almost an

insult to her high spirited pride, to her love, which had humiliated
itself by the first confession on that night in the deserted ballroom
where she had poured out the wretchedness of her soul. She had
come to him wounded, homeless, and he had all but cast her off in
his passionate selfishness, his hatred of the loveless marriage which
his honor had bound him to make.
If he had only loved her, if he had but dissembled and seemed to
love her! Overwhelmed with grief he searched his mind for one
reassuring recollection, for one instance which should acquit him of
complicity in the tragic agony of her death, but he found none. He
had neglected her, denied her, tried to evade that final moment
when he must ask her to be his wife, and through all she had borne
with him with a sweetness unusual in her stormy nature; she had
loved him well enough to make allowances, to forgive, to overlook!
And now passing away from him without a word, she had left only
her final kiss of forgiveness on his cheek, the wild rush of her tears
at their last parting. Henceforth he should never speak to her again,
never hear her voice, never know how deeply she had suffered,
never ask her forgiveness. The fact that the sequence of events was
inevitable, that a woman no sooner seeks a man’s love than she
loses it, gave him no relief. In his own eyes he had been little short
of a monster of cruelty to a dying woman because, forsooth, he
loved another—younger and more beautiful!
Memory, too, tormented him with the thought of Margaret, young,
sweet, confiding as she had been when he had first known her and
loved her; he thought less of the moment when she broke faith and
married White; her fault was less now than his; the error of a
beautiful, wilful girl seemed but a little thing before the awful fact of
her wrecked life, her tragic death. Through all she had really loved
him, that one thing seemed certain; her spirit in all its wild sweet
waywardness had held to this one tie, her love for him, and when
she had turned to him at last in her wretchedness seeking
happiness, asking it, pleading for it like a child, she had received not
bread but a stone! He knew now that no living woman could have

misunderstood his coldness, his tardiness, his indifference, and in his
cousin’s pale and averted face he read an accusing understanding.
He threw himself into a chair again and sat staring gloomily at the
floor. “What madness!” he exclaimed at last, with sudden fury; “how
dared Gerty neglect her so? She was ill, weak, unprotected!”
“Gerty was no more to blame than others,” Allestree observed
quietly.
Fox threw back his head haughtily, and their eyes met. “I was willing
to give her my life,” he said bitterly, “I had no more to give!”
Allestree rose. “It is over,” he replied gravely; “we cannot bring her
back; come, you will go there, she would wish it, I know,” he added,
“and there is no one else!”
The awful finality of those words and the reproach they carried was
indisputable. Fox rose with a deep groan and went out with him,
without a word, to face the greatest trial of all.

VIII
IN a little pension on the rue Neuve des Petits Champs, Rose Temple
had been working patiently at her music for six months and more,
studying under one of the great Italian teachers, a man who had
trained more than one prima donna and was, therefore, chary of his
encouragement. The enthusiasm which she had brought to her task
having been gradually dispelled by sharp disappointments, she had
struggled on, determined to succeed at last.
The first test of her voice before the maestro and his French critics
had been a failure, a failure so complete that she came home to
weep her heart out on the faithful shoulder of the elderly cousin who
was her chaperon and comforter. The weakness of a voice, beautiful
but not yet fully trained, her trepidation at singing before the
maestro and his assembled judges, together with the long strain of
preparation, had united in her undoing. She came back to the
pension without a word of encouragement, feeling at heart that she
would never sing a note again.
She sat down, laying her head on the little writing-table, amid a wild
confusion of Miss Emily Carter’s pens and papers, and gave way to
her despair. “I shall never sing again!” she said, “never—I’m a
miserable failure; I haven’t any more voice than a sparrow, and
there’s all that money wasted, thrown away!”
Miss Emily eyed her quietly. She had the intense family pride which
is nurtured in the State of Virginia; she did not need to be told, she
knew that Rose had the loveliest voice in the world. As for these
nasty, little, fat, insinuating Frenchmen! She took off her spectacles
and smoothed her hair back from her temples; it was done as they
did hair forty years ago; it matched her immaculate turn-over lace
collar and hair brooch. “You’ll blot my letter, Rose,” she said calmly,
with a little drawl that was inimitable; “I don’t see what you’re crying
about, it will make your nose red; as for these horrid little Parisians,

they know about as much about you as they do about heaven—
which isn’t enough to get there!”
In spite of herself Rose laughed feebly. “You’re the most prejudiced
person I know, Cousin Emily!”
“Prejudiced?” Miss Carter’s nostrils quivered scornfully, “I wasn’t
raised within forty miles of Richmond for nothing, Rose Temple!
Don’t you suppose I know a gentleman when I see one? What in the
world can you expect from that person if he is a singing master? He
wears a solitaire ring on his little finger and a red necktie. I reckon
I’ve got eyes if I do wear spectacles.”
“But he’s trained half the great singers of the world, Cousin Emily,
and at first he was so kind about my voice—to-day—” Rose winked
back the hot tears—“to-day he never said a word!”
“Pig!” ejaculated Miss Carter unmoved.
Rose laughed hysterically. “I shall never sing; I’d better take to
washing and ironing for a living!”
“You’d make a fortune,” retorted Miss Carter ironically; “while you
were mooning you’d scorch all the shirt bosoms and smash the
collars.”
“You’re not a bit encouraging; no one is!” Rose said helplessly,
leaning back in her chair; “it makes my heart ache to think of
wasting poor father’s money so!”
“And I reckon he’d give the whole of it to keep your little finger from
hurting; he thinks you’re a chip of the moon. And how in the world
do you know you’ve wasted it yet?” continued her cousin, calmly
indignant; “perhaps you didn’t sing well to-day; is that any reason
you won’t to-morrow?”
Rose looked at the angular figure opposite, and the color came again
slowly to her cheeks and the light to her eyes. “I’m so glad you
came, Cousin Emily!” she exclaimed; “without you I should have just
given up, they looked so—so indifferent, those men with their eye-
glasses and their notebooks and their stare.”

“Stare? I should think so!” replied Miss Carter severely; “I’ll put a
Frenchman against anything for staring. I believe myself that Paris is
a Sodom and Gomorrah boiled into one, let me tell you! How any
nice sweet girl can marry one of them— Rose, if anything should
ever induce me at any time to think of marrying one, clap me into
an insane asylum, you hear?”
And Rose, burying her face in her hands, laughed until she cried.
But without Miss Carter and Aunt Hannah her courage would have
failed her often in the months which followed. She was put back at
the alphabet of music and worked with the beginners. More than
one night she secretly cried herself to sleep without daring to tell
Cousin Emily of her weakness. Homesickness, too, pinched her and
took the color from her cheeks, but she worked bravely on. She had
reached Paris in June and she had failed at her trial in September.
The months which followed were crowded to the brim, and she tried
to shut her heart and her ears to news from home, except that
which concerned her father. The judge’s letters were purposely
cheerful and optimistic, he said so little about financial difficulties
that it seemed like a troubled dream to Rose; she never quite
realized all it meant to her future.
At last, after many months, her instructor told her one morning that
he should bring some competent judges to hear her again and, if
she succeeded at this second test, he should try to give her a great
opportunity to win her place in the world as a singer. Rose’s heart
thrilled. The great man said little, but at last she perceived that he
believed in her in spite of her failure, that her voice had finally won
his confidence. A word from him was more than a volume from
another; it meant success or failure. The girl, full of her dreams of
singing and redeeming all with her voice, trembled all over and
turned pale. There was a great excitement at the little pension that
night; confident though she was, Miss Carter secretly wiped away a
tear, and they both worked late to give some fresh touches to the
girl’s white gown which brought it up to date; it was a year old, and
not made in Paris! They began to see such differences, to recognize

the enchanting creations in the show-windows and out walking on
the fashionable women on the boulevards.
However, Cousin Emily had her opinion about its owner’s appearance
in that same old white frock, and she stole out and bought a single
rose for the young singer to wear the next afternoon. Aunt Hannah
helped dress her; it was a great occasion; the little flat looked as
though a whirlwind had struck it, and at last the two went out in
great trepidation to keep the appointment. Secretly Miss Emily
longed to give those Frenchmen a piece of her mind about criticizing
the voice of a sweet young girl, but she only retired discreetly to a
corner and looked on with a peculiar moisture on her spectacles
which required the constant use of her handkerchief.
As Rose ceased singing and the last clear notes of her voice floated
into the distances of the great empty concert-hall, the thrill of its
sweetness, its purity, its young confident power, seemed to fill the
very atmosphere of the place with exquisite music; it could not quite
pass away into silence, it remained at last, if not in the ears, in the
souls of the listeners, a little group to the right of the stage who had
gathered there to hear the wonderful pupil, his youthful prima
donna, the great gift which, he believed, the new world had for the
old.
In the midst of her song she had forgotten herself, her audience, her
first failure, even the world itself, while her young ardent soul
poured out its joy and its grief in those splendid notes. Love, that
great interpreter of the heart, had unlocked hers to sorrow, she sang
with the heart of the sorrowful; she was, first of all, as Allestree felt,
an impersonation of youth, and she sang with the soul of youth
which hopes forever; she loved, purely, unselfishly, gently, and she
sang with the love of the world on her lips, and singing thus was
supremely lovely; what matter if the old white dress was a little out
of fashion? She was a figure as symbolic of youth with its splendid

hopes, its faith, its untried strength, as she was the very
personification of beautiful womanhood.
No one spoke, no one applauded, but not an eye was dry.
But to Rose, whose ears were not filled with her own music, the
silence which followed it came with a shock of terrible revulsion. She
waited a moment in keen suspense, but no one spoke, no one
moved; the wave of silence that followed the wave of sound
engulfed her hopes, she remembered that first disappointment.
Bitter dismay swept over her, she turned away to hide her emotion,
but the maestro crossed the stage at that instant and held out his
hand; he could not praise her but there was actually a tear in his
eye.
Rose looked up, and reading his face burst into tears of joy, her
hopes suddenly fulfilled.
Then the party of judges broke out with a round of applause and
one little Frenchman, with a polished pink bald head and mustaches,
shouted: “Brava!”
In the end they crowded around her and overwhelmed her with
compliments; they were eager to invite her to a supper and drink
her health in champagne, but the staid Virginia cousin, in the old-
fashioned black bonnet and the old black alpaca gown, which
outraged Paris without hiding the good heart beneath it, frowned on
this hilarity; her deep-seated suspicion of the Parisian in general had
not been dissipated by this burst of applause. She insisted that Rose,
who was trembling with excitement and the strain of the long hours
of training, should go straight back to their little apartment to rest. A
decision too full of wisdom for even Rose, eager though she was for
the sweet meed of praise, to resist it.
They drove back in a fiacre, a wild extravagance which they
ventured in view of the great success and the immediate prospects
of a fortune; the cousin felt that they were immediate.
“You all were always talented,” she said to Rose, as they drove down
the rue de Rivoli; “your mother could do anything; we always said

so. Cousin Sally Carter, too, is going to be an artist, and no one ever
made preserves like Cousin Anna’s! I reckon it’s in the family, Rose.”
“Oh, Cousin Emily!” Rose sighed, and hid her face on the alpaca
shoulder, “oh, if I can only, only sing so well that there shall be no
more terrible trouble for father!”
“Now, don’t you worry about the judge, child,” Cousin Emily replied
soothingly; “it will all come out right and, anyway, the best families
haven’t money now-a-days!” she added with ineffable disdain, “it’s
very vulgar.”
“I think I’d risk having it, though!” Rose said, with a sigh.
She was really in a dream. The softness of spring was in the
atmosphere as they drove through the gay streets, and all the trees
in the garden of the Tuileries were delicately fringed with green; the
voices of children, the sounds of laughter, now and then a snatch of
song, reminded them that it was a holiday. Rose thought of home;
the Persian lilac must be budding, the tulip trees, of course, were in
flower; a pang of homesickness seized her, a longing to see the old
house again—ah, there was the sorrow of it, could they keep the old
house much longer? With these thoughts came others, deeply
perturbed, which she tried to thrust away. She knew of Margaret’s
sudden death, but she had heard but little of it, of Fox nothing. Her
father’s letters excluded the whole matter; Mrs. Allestree’s were
chary in mention of it, and from Robert there was no word on the
subject. Gerty English, strangely enough, had not written since
Margaret’s death, and Rose could only piece together the dim
outlines of a tragedy which touched her to the soul. There had been
moments when she had been bitter against poor Margaret, had held
her responsible, now she thought of her with pity.
As these things floated before her, in a confused dream of sorrow
and regret, she was scarcely conscious of Cousin Emily’s chatter, or
of the streets through which they passed, but presently they were
set down at their own door and she paid the cabman; Cousin Emily’s
French was excellent but it belonged exclusively to the classroom

and the phrase-book, and no one in Paris understood it, a fact which
bewildered her more than any of her other experiences.
They found the pension disturbed by a fire in an adjoining house,
and Aunt Hannah was sitting on top of Rose’s trunk with her bonnet
on, waiting to be assured that the flames could not reach her.
“It’s all out, Aunt Hannah,” Rose assured her, laughing; “the
concierge says it was out half an hour ago.”
“He don’ know nuthin’ about it, Miss Rose; he ain’t sure dat he’s a
liar, an’ I knows he is, bekase I’se caught him at it,” the old woman
replied firmly; “de place might be afire sure nuff. It was one ob dem
’lection wires dat set de odder house off, an’ dis place is full ob dem;
I don’ tole him ter cut ’em loose, an’ he keep on jabberin’ like a
monkey; I ain’t got no manner ob use fo’ dese French people no-
ways!”
“Nor has Cousin Emily!” laughed Rose, taking off her hat and tossing
it to Aunt Hannah, while she passed her hand over her bright hair
with a light, deft touch which seemed to bring every ripple into a
lovelier disorder; “the poor concierge is a good soul, and he does
make us comfortable here.”
“Mebbe he is, an’ mebbe he ain’t!” said Aunt Hannah grudgingly;
“dese men folks allus waits on a pretty girl, honey, but I ’lows he’d
cheat yo’ jest de same; I’se got my eye on him sure!”
“I wish you’d take off your bonnet and get my trunk open,” retorted
Rose good naturedly; “then we’ll see if we can put the concierge in it
—if he misbehaves!”
“My sakes, honey, I done clean forgot ter gib yo’ dis letter; it’s a
telegram, I reckon; it come jest befo’ de fire broke out, an’ I’se been
settin’ on it ter keep it safe.”
It was a cablegram, and Rose stretched out an eager hand for it,
with a thrill of anticipation; it seemed as if her father must be
reaching out to her across the seas, that he already knew and

rejoiced with her for, surely, all his prejudices would dissolve at the
assurance of her success.
She opened it with trembling fingers, a smile on her lips. It fluttered
and fell to the floor; it was a cablegram to summon her home, the
judge was very ill.

IX
AFTERWARDS Rose never quite knew how she endured the voyage
home. Her love for her father was so deep, so tender, they were so
bound together by a hundred ties not only of affection but of
sympathy and tastes and interests, that the very thought of losing
him almost broke her down. It took both Cousin Emily Carter and old
black Aunt Hannah to comfort and sustain her during those ten
days.
But when she reached Washington Allestree met her at the station
with good tidings; the judge was out of danger. He had been very
near death and came back slowly from the Valley of the Shadow.
However, he had come back and Rose knelt beside his bed and cried
her heart out with joy to feel his arm around her. How pale and thin
and wasted he looked. He had aged so much; poor Rose, she saw it
and forced a smile to disguise it even to herself. But he was unaware
of the shock which the sight of him gave her, and he forgot his
illness in his eager interest in her account of Paris and her final
success. She told him very little of those long months of struggle
and depression, of the thousand little pinches and trials that they
had been through to keep from asking an extra penny from him.
After Rose came the judge began to mend more rapidly; old Mrs.
Allestree said he had only been pining away for the child, but she
knew better, being a wise old woman. She knew that the judge had
been struggling all the year to stave off the foreclosure of the
mortgage on the old house which he and Rose loved so well. She
knew, too, that he had almost failed when that mysterious
arrangement was made for him by an unknown party; the message
came that the mortgage had been taken up, and he could have all
the time he wanted and at a lower rate of interest.
This news, so amazing and so unprecedented, had been
synchronous with the judge’s breakdown and had, Mrs. Allestree
believed, contributed to it. The sudden relief had snapped the strain

on his nerves, and he slipped down into a state of coma. However,
she did not tell Rose this, nor her suspicions, which were fast
becoming certainties, about the mortgage; she only kissed her
affectionately and made her sing to her the song which had won
such an ovation from the French critics, and which Cousin Emily
Carter had described with enthusiasm before she departed to the
Tidewater region, where she hoped to cut her own asparagus bed
and set out her flowers undisturbed by Parisian manners and
customs.
Allestree welcomed Rose with even greater relief than his mother
and the judge, but wisdom had taught him to rejoice in silence, and
he did so, being careful, however, to send promptly for her portrait
which, according to the agreement between Mrs. Allestree and the
judge, could not be loaned during Rose’s presence in the house, but
only as a consolation in her absence. But the judge sighed deeply
when they told him it had been returned to the studio again.
It was during the first days of her father’s convalescence that Rose
found Margaret’s letter to her among his papers; not knowing Rose’s
address in Paris, Margaret had sent it in the judge’s care and he had
overlooked it when he forwarded the letters, as he did, once a week.
By a strange accident it had slipped under some pamphlets in the
basket on his library table and lay there until Rose, rearranging his
papers one morning, came upon it and recognizing the writing broke
the seal with some trepidation, for Margaret had never been an
intimate correspondent, and Rose divined some serious reason for
this long closely written letter. She was alone when she found it, and
she went to the open window and stood there reading it.
Margaret, moved by the deep sorrow and passion which had swept
over her poor troubled soul in those last days of her life, had poured
out her heart. She told Rose all; that she had come between her and
Fox; in her wild and covetous jealousy she had thought to wrest
happiness from despair; to keep his love she had been willing to lose
all, and she had lost! She concealed nothing, the last pitiful words of
the letter, a remarkable letter of passion and grief and self-sacrifice,

told Rose that she was going to give up her life to her children and
try to live down her desertion of them.
Rose read it through to the end, and then covered her face with her
hands, trying to shut out the terrifying picture that it had
unconsciously drawn of a woman, desolate, shipwrecked, without
hope in earth or heaven. The terrors which had possessed
Margaret’s soul swept over hers. All that Mrs. Allestree had told her,
and that Gerty, poor, voluble, good-hearted Gerty, had enlarged
upon, filled out the scene. The lonely walk, the visit to the studio,
the unfriended and miserable death; she did not know of those other
scenes in the church and the curiosity-shop where Margaret had
found her heart, but she did know of a strange girl who had brought
a single white lily to lay in Margaret’s dead hand and gone away
weeping bitterly.
She had blamed poor Margaret, judged her; Rose felt it at that
moment and accused herself of heartlessness; of Fox she dared not
think. In the new light which this letter shed on the situation, she
began to understand how cruelly he had been placed, and there,
too, she had judged!
Poor Rose,—her father had inculcated stern and simple lessons and
she had tried, before all things, to be just; but to be judicious and
calm and in love at the same time was an impossible combination.
She dashed the tears from her eyes, and thrust Margaret’s letter into
her pocket and went about her duties with the air of a soldier on
guard, but her lip would quiver at intervals and she could not sing a
note when the judge asked for one of the old ballads that he had
loved as a boy, and Rose had learned, to please him.
It was about this time that she began to wonder if the old house
must go, or if her father had been able to meet all the payments due
upon it. She dared not ask him, and he said nothing, but she noticed
that now that he was able to be moved into the library every day
and sometimes into the garden in the warm spring sunshine, that he
sat for hours at a time in a brown study with a deep furrow between
his brows, and constantly pushing back his hair from his forehead,

Welcome to our website – the ideal destination for book lovers and
knowledge seekers. With a mission to inspire endlessly, we offer a
vast collection of books, ranging from classic literary works to
specialized publications, self-development books, and children's
literature. Each book is a new journey of discovery, expanding
knowledge and enriching the soul of the reade
Our website is not just a platform for buying books, but a bridge
connecting readers to the timeless values of culture and wisdom. With
an elegant, user-friendly interface and an intelligent search system,
we are committed to providing a quick and convenient shopping
experience. Additionally, our special promotions and home delivery
services ensure that you save time and fully enjoy the joy of reading.
Let us accompany you on the journey of exploring knowledge and
personal growth!
ebookfinal.com

Network aware source coding and communication 1st Edition Nima Sarshar

More Related Content

Similar to Network aware source coding and communication 1st Edition Nima Sarshar

Recently uploaded

Network aware source coding and communication 1st Edition Nima Sarshar