Improved Linear Programming Decoding using Frustrated Cycles

TL;DR

This paper introduces an improved linear programming decoding method for low-density parity-check codes over Gaussian noise channels by identifying and adding frustrated cycles to enhance decoding accuracy.

Contribution

It presents a systematic algorithm to identify frustrated cycles causing fractional solutions and adaptively incorporates them to improve decoding performance.

Findings

Enhanced decoding accuracy over traditional LP decoding

Identification of frustrated cycles as key to fractional solutions

Improved word error rate performance

Abstract

We consider transmission over a binary-input additive white Gaussian noise channel using low-density parity-check codes. One of the most popular techniques for decoding low-density parity-check codes is the linear programming decoder. In general, the linear programming decoder is suboptimal. I.e., the word error rate is higher than the optimal, maximum a posteriori decoder. In this paper we present a systematic approach to enhance the linear program decoder. More precisely, in the cases where the linear program outputs a fractional solution, we give a simple algorithm to identify frustrated cycles which cause the output of the linear program to be fractional. Then adding these cycles, adaptively to the basic linear program, we show improved word error rate performance.