Bidirectional sequential decoding

Abstract

The main drawback of sequential decoding is the variability of its decoding effort which could cause decoding erasures. We propose and analyze an efficient bidirectional sequential decoding (BSD) technique to alleviate this drawback. In the proposed BSD, two decoders are used; one is called a forward decoder (FD), and is used to search the tree from the forward direction; while the other is called a backward decoder (BD), and is used for the backward search of the tree. Forward decoding and backward decoding are performed simultaneously, and stop whenever the FD and BD merge at a common encoder state somewhere in the tree. The relationships between backward coding and forward coding are examined in detail. Good rate 1/2 convolutional codes, with memory m ranging from 2 to 25, suitable for bidirectional decoding found through extensive computer search, are provided. These codes possess the same distance properties from both forward and backward directions. It is found, by means of extensive computer simulations as well as a heuristic argument, that the advantage of the BSD appears as a substantial decrease of the computational variability of the sequential decoding. Our findings suggest that the Pareto exponent of unidirectional sequential decoding (USD) can be practically doubled by using BSD.