A directed search approach for unit-memory convolutional codes

Abstract

A set of heuristic algorithms to numerically search for binary unit-memory convolutional codes (UMC) are presented along with a large number of new codes for 2/spl les/k/spl les/8 and code rate 1/4/spl les/R<1. Combinatorial optimization is used which involves selecting and then pairwise-matching column vectors of the two (n,k) UMC tap weight matrices. The column selection problem is that of finding the best (2n,k) binary, linear block code (BC). In this correspondence, the best BC generator matrix G is found by successively refining G using directed local exhaustive searches. In particular, the set of minimum-weight codewords are used to find a subset of G to exhaustively search. The UMC search strategy (pairwise matching problem) uses a directed local exhaustive search similar to the BC directed search by using the concept of the terminated BC of the UMC. The heuristic algorithms developed in this correspondence are very robust and converge relatively quickly to the optimal or near-optimal UMC. In addition, although it is generally possible to achieve the block code upper bound for free distance, we give a class of UMCs which cannot achieve this bound.