CodingandErrorControl.pptVIP

Coding and Error Control Chapter 8 Coping with Data Transmission Errors Error detection codes Detects the presence of an error Automatic repeat request (ARQ) protocols Block of data with error is discarded Transmitter retransmits that block of data Error correction codes, or forward correction codes (FEC) Designed to detect and correct errors Error Detection Probabilities Definitions Pb : Probability of single bit error (BER) P1 : Probability that a frame arrives with no bit errors P2 : While using error detection, the probability that a frame arrives with one or more undetected errors P3 : While using error detection, the probability that a frame arrives with one or more detected bit errors but no undetected bit errors Error Detection Probabilities With no error detection F = Number of bits per frame Error Detection Process Transmitter For a given frame, an error-detecting code (check bits) is calculated from data bits Check bits are appended to data bits Receiver Separates incoming frame into data bits and check bits Calculates check bits from received data bits Compares calculated check bits against received check bits Detected error occurs if mismatch Error Detection Process Parity Check Parity bit appended to a block of data Even parity Added bit ensures an even number of 1s Odd parity Added bit ensures an odd number of 1s Example, 7-bit character [1110001] Even parity Odd parity Cyclic Redundancy Check (CRC) Transmitter For a k-bit block, transmitter generates an (n-k)-bit frame check sequence (FCS) Resulting frame of n bits is exactly divisible by predetermined number Receiver Divides incoming frame by predetermined number If no remainder, assumes no error CRC using Modulo 2 Arithmetic Exclusive-OR (XOR) operation Parameters: T = n-bit frame to be transmitted D = k-bit block of data; the first k bits of T F = (n – k)-bit FCS; the last (n – k) bits of T P = pattern of n–k+1 bits; this is the predetermined divisor Q = Quotient R = Rem