Efficient Linear Programming Decoding of HDPC Codes

TL;DR

This paper introduces improved LP decoding algorithms for HDPC codes, utilizing automorphism groups, mixed integer decoding, and adaptive techniques to achieve near-ML performance with manageable complexity.

Contribution

It presents novel methods including automorphism-based parity check diversity, an efficient branch-and-bound decoder, and adaptive matrix adjustments for enhanced decoding.

Findings

Decoders achieve near-ML performance

Automorphism groups improve decoding efficiency

Adaptive techniques reduce complexity

Abstract

We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts from redundant parity checks. Second, we propose an efficient mixed integer decoder utilizing the branch and bound method. We further enhance the proposed decoders by removing inactive constraints and by adapting the parity check matrix prior to decoding according to the channel observations. Based on simulation results the proposed decoders achieve near-ML performance with reasonable complexity.