On computing undetected error probabilities on the Gilbert channel

The authors examine methods for computing the probability of undetected error on the Gilbert channel. First, using Monte Carlo simulation they study the standard cyclic redundancy codes and compare the results with those on the binary symmetric channel. Then the authors consider a general method of approximate code evaluation which involves P(m,n), the probability of m errors in a block of length n bits. A nonrecursive technique for computing P(m,n) on the Gilbert channel is derived. Finally, it is shown how the symmetries of the Gilbert channel can lead to useful results for dealing with cyclic codes