On the undetected error probability of linear block codes on channels with memory

We give an upper band on the undetected error probability of binary (n,k)-codes used on channels with memory described by Markov distributions. This bound is a generalization of the bound presented by Kasami (1983) for the binary symmetric channel (BSC). An extended bound is given for the Gilbert-Elliott channel (1960, 1963) and Markov channels with deterministic errors. We also develop a recursive technique for the exact calculation of the undetected error probability of an arbitrary linear block code used on a Markov type channel. This technique is based on the trellis representation of block codes described by Wolf (1978). Results of the computations are presented