An optimization algorithm for estimating the storage requirements of a reduced-search decoder

A classical problem in reduced-search channel decoding has been the accurate estimation by computational or analytical means of the smallest code search that attains a set performance. The problem is particularly difficult for breadth-first decoders (i.e, decoders without balancing), that work from a fixed size storage of trellis paths. An obvious measure of performance is the overall bit error rate. An easier measure to analyze is the distance attainable in a bounded-distance decoder. If the decoder is to correct all channel noises of length or weight less than d what size storage does it need? We define an optimization problem whose solution is this maximum size, propose a solution based on a contraction mapping, and give numerical results for ordinary convolutional and partial-response codes