FErrorControlCoding.pptVIP

3F4 Error Control Coding Dr. I. J. Wassell Introduction Error Control Coding (ECC) Extra bits are added to the data at the transmitter (redundancy) to permit error detection or correction at the receiver Done to prevent the output of erroneous bits despite noise and other imperfections in the channel The positions of the error control coding and decoding are shown in the transmission model Transmission Model Error Models Binary Symmetric Memoryless Channel Assumes transmitted symbols are binary Errors affect ‘0’s and ‘1’s with equal probability (i.e., symmetric) Errors occur randomly and are independent from bit to bit (memoryless) Error Models Many other types Burst errors, i.e., contiguous bursts of bit errors output from DFE (error propagation) common in radio channels Insertion, deletion and transposition errors We will consider mainly random errors Error Control Techniques Error detection in a block of data Can then request a retransmission, known as automatic repeat request (ARQ) for sensitive data Appropriate for Low delay channels Channels with a return path Not appropriate for delay sensitive data, e.g., real time speech and data Error Control Techniques Forward Error Correction (FEC) Coding designed so that errors can be corrected at the receiver Appropriate for delay sensitive and one-way transmission (e.g., broadcast TV) of data Two main types, namely block codes and convolutional codes. We will only look at block codes Block Codes We will consider only binary data Data is grouped into blocks of length k bits (dataword) Each dataword is coded into blocks of length n bits (codeword), where in general nk This is known as an (n,k) block code Block Codes A vector notation is used for the datawords and codewords, Dataword d = (d1 d2….dk) Codeword c = (c1 c2……..cn) The redundancy introduced by the code is quantified by the code rate, Code rate = k/n i.e., the higher the redundancy, the lower the code rate Block Code - Example Dataword length k = 4 Codeword le