The distribution of the sequential decoding computation time

Previous studies of sequential decoding algorithms have shown that the computation time required per decoded digit is small, on the average, when the source rate is less than a rate . In this paper, we consider the probability distribution of the computation time per decoded digit for the Fano algorithm on the binary symmetric channel. We show by underbounding this distribution that it behaves as , in the distribution parameter , that is, it is of the Pareto type. We deduce from this fact that the probability of overflowing the buffer required to store data during periods of high computation is relatively insensitive to the buffer storage capacity and to the maximum speed of the accompanying logic unit. It is shown that this lack of sensitivity exists because the computation per decoded digit is large during intervals of high channel noise and grows exponentially with the length of such an interval. The overflow probability, however, is a strong function of the source rate and is more than squared by a halving of this rate.