An Upper Bound for the Error Probability on the Gilbert Channel

The binary symmetrical channel with memory (Gilbert model) allows a satisfactory approximation of the error distribution on real channels characterized by error bursts. Its use is, however, relatively limited due to the computing involvemeats, which usually lead to the programming of the respective problems on a computer. Two manners of simplifying the computation of the probability
P(m,n)
of
m
errors in a code word of length
n
, are shown. The first manner is based on deducing a direct relation by means of the method of the generating function and simplifying it on the basis of the existing inequalities among the usual values of the Gilbert channel parameters. The second manner is based on deducing an upper bound for the
P(m,n)
probability on the Gilbert channel. The formulas deduced allow simplification of the computation of the performance of the error correcting and detecting codes on the Gilbert channel.