Improving the Performance of LP Decoders for Cyclic Codes

Abstract

Recently, a linear programming (LP) decoder has been introduced for binary linear codes. Although the performance of an LP decoder has a close relationship with the form of the parity check matrix (or equivalently with the Tanner graph) of the code, there is no clear approach to choosing a suitable form for LP decoding. In this paper, we focus on the class of cyclic codes, and show that the cyclic structure of the code can be used to expand the parity check matrix and obtain a low redundancy form which is suitable for LP decoding. Performance results are given which demonstrate the effectiveness of the proposed algorithm.