Using combinatorial optimization to design good unit-memory convolutional codes

A method for designing good unit-memory convolutional codes is presented. The method is based on the decomposition of the original problem into two easier subproblems that can be formulated as optimization problems and solved by efficient heuristic search algorithms. The efficacy of this method is demonstrated by a table containing 33 new unit-memory convolutional codes (n,k) with 5⩽k⩽8, rates R= k/n between 1/4 and 7/9, and complete memory (M =k), as well as 12 new linear block codes. Most of the codes found have minimum free distance