Sequential Decoding with a Look-Ahead Path Metric

Abstract

Convolutional codes are an efficient means of achieving reliable communication with low latency and complexity constraints. Since optimal Viterbi decoding of long (say, above 8) constraint length codes can be prohibitively complex, sequential decoders, such as the Zigangirov-Jelinek (ZJ) stack algorithm or the Fano algorithm can be applied. However, the performance of sequential algorithms is limited by a steep increase in the average number of steps per information bit that takes place close to the cutoff rate, more than by the error correcting capabilities of the code itself. In this paper we examine the problem of improving the performance of sequential decoders by designing more sophisticated path metrics. In particular, we propose a look-ahead (LA) path metric, which equals the Fano metric of the best path stemming from the current path for a fixed number of time steps. We demonstrate that in the limit of a large number of look-ahead time steps, sequential decoding becomes equivalent to the backtracking step of the Viterbi algorithm. Direct computation of the LA metric requires searching an exponential number of partial paths at each state and is infeasible, since the extra cost of computing the metric outweighs the savings in the number of time steps. However, in some scenarios of interest, the LA metric can be computed by other means. In the particular case of a covolutional code transmitted over a binary symmetric channel (BSC), this metric can be obtained from a modified syndrome decoder that stores for each partial syndrome the weight of the minimum weight error event. We demonstrate through simulations that this structure leads to an efficient and computationally inexpensive sequential decoding algorithm.