Sequential decoding based on an error criterion

An analysis of sequential decoding is presented that is based on the requirement that a set probability error P_e be achieved. The error criterion implies a bounded tree or trellis search region: the shape of this is calculated for the case of a binary symmetric channel with crossover probability P and random tree codes of rate R. Since the search region is finite at all combinations of p and R below capacity, there is no cutoff rate phenomenon for any P_e>0. The decoder delay (search depth), the path storage size, and the number of algorithm steps for several tree search methods are calculated. These include searches without backtracking and backtracking searches that are depth- and metric-first. The search depth of the non-backtracking decoders satisfies the Gallager reliability exponent for block codes. In average paths searched, the backtracking decoders are much more efficient, but all types require the same peak storage allocation. Comparisons are made to well-known algorithms