Linear-programming Decoding of Non-binary Linear Codes

TL;DR

This paper introduces a linear-programming decoding framework for non-binary linear codes over rings, demonstrating its optimality and performance comparable to traditional hard-decision decoding for a specific ternary Golay code.

Contribution

It develops a novel LP decoding method for non-binary codes, proves its maximum likelihood certificate property, and establishes equivalence with graph cover pseudocodewords.

Findings

LP decoder has maximum likelihood certificate property

Decoder output is the lowest cost pseudocodeword

Performance comparable to codeword-error-rate-optimum hard decoding

Abstract

We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' property, and we show that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. LP decoding performance is illustrated for the (11,6,5) ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the LP decoder performance is comparable to codeword-error-rate-optimum hard-decision based decoding.