Parity check, redundancy, and errors
- 2. TABLE OF CONTENTS COVER PAGE………………………….slide 01 NAMES OF PARTICIPANTS…………. slide 03 TYPES OF ERRORS………………….. Slide 04 REDUNDANCY………………………. Slide 05 ERROR DETECTION AND CORRECTION slide 06
- 3. TYPES OF ERRORS 1) SINGLE BIT ERROR The term single-bit error means that only 1 bit of a given data unit (such as a byte, character, or packet) is changed from 1 to 0 or from 0 to 1.
- 4. TYPES OF ERRORS cont… BURST ERROR The term burst error means that 2 or more bits in the data unit have changed from 1 to 0 or from 0 to 1.
- 5. REDUNDANCY The central concept in detecting or correcting errors. To be able to detect or correct errors, we need to send some extra bits with our data. These redundant bits are added by the sender and removed by the receiver. Their presence allows the receiver to detect or correct corrupted bits.
- 6. ERROR DETECTION AND ERROR CORRECTION ERROR DETECTION is the process of monitoring data transmission and determining when errors have occurred. Error- detection techniques neither correct errors nor identify which bits are in error they indicate only when an error has occurred. ERROR CORRECTION Is the process of recovering or removing errors in transmitted signal of information. This is mainly done at the receiver.
- 7. BLOCK CODING The message is divided into blocks Each block is k-bits size, called dataword add r redundant bits to each block The resulting n-bit blocks are called codewords. n = k + r 2^n – 2^k (illegal or invaild codewords)
- 8. BLOCK CODING cont…… An error-detecting code can detect only the types of errors for which it is designed; other types of errors may remain undetected.
- 9. PARITY CHECK Parity Check The simplest error-detecting scheme is to append a parity bit to the end of a block of data. A typical example is character transmission, in which a parity bit is attached to each 7-bit IRA character. The value of this bit is selected so that the character has an even number of 1s (even parity) or an odd number of 1s (odd parity).
- 10. HAMMING DISTANCE Is the number of difference between the corresponding bits. d(x,y) The minimum Hamming distance is the smallest Hamming distance between all possible pairs in a set of words. Any coding scheme needs at least three parameters
- 11. HAMMING DISTANCE cont….. (i)Code word size n (ii)Data word size k (iii)d min The hamming distance between the sent and received code words is the number of bits affected To guarantee the detection of up to s errors in all cases, the minimum Hamming distance in a block code must be dmin= s + 1.
- 12. CYCLIC REDUNDANCY CHECKING One of the most common, and one of the most powerful, error-detecting codes is the cyclic redundancy check (CRC), which can be described as follows. Given a k-bit block of bits, or message the transmitter generates an (n-k) bit sequence, known as a frame check sequence (FCS), such that the resulting frame, consisting of n bits, is exactly divisible by some predetermined number. The receiver then divides the incoming frame by that number and, if there is no remainder, assumes there was no Error.
- 13. CHECKSUM CHECKSUM is another relatively simple form of redundancy error checking where each character has a numerical value assigned to it. The characters within a message are combined together to produce an error-checking character (checksum), which can be as simple as the arithmetic sum of the numerical values of all the characters in the message.
- 14. FORWARD ERROR CORRECTION Forward error correction (FEC) is the only error- correction scheme that actually detects and corrects transmission errors when they are received without requiring a retransmission. With FEC, redundant bits are added to the message before transmission. When an error is detected, the redundant bits are used to determine which bit is in error