Estimates of Error Rates for Codes on Burst-Noise Channels
01 September 1963
The structure in hursts of noise on real communication channels is usually very difficult to describe. As a consequence, no general procedure exists for predicting the performance of error detecting or error correcting codes, and no basic set of parameters exists for describing the channel. Gilbert1 has shown that a simple Markov model with three parameters provides a close approximation to certain telephone circuits used for the transmission of binary data. When such an approximation is possible, the error rates for codes may be easily calculated from these channel parameters and properties of the code. (See Section V.) To provide a means for estimating error rates for binary block codes in more general circumstances, a table of probabilities P(m,n) may be employed. P(m,n) is the probability that m bit errors occur in a transmitted block of n bits. It was speculated and later corroborated (as we will show) that equivalent error detecting codes would have rather comparable error rates when employed on the same channel. (Two codes are equivalent if one may be obtained from the other by a permutation of bit positions.) Thus the average error rate for all codes equivalent to a 1977