Efficient Linear Programming Decoding of HDPC Codes
Alex Yufit, Asi Lifshitz, Yair Be'ery

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.
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