Linear-Programming Decoding of Nonbinary Linear Codes
Mark F. Flanagan, Vitaly Skachek, Eimear Byrne, Marcus Greferath

TL;DR
This paper develops a linear-programming decoding framework for nonbinary linear codes over rings, demonstrating its theoretical properties, complexity advantages, and comparable performance to traditional decoding methods in simulations.
Contribution
It introduces a novel LP decoding framework for nonbinary codes, proves key properties, and shows polynomial-time decoding with performance comparable to optimal methods.
Findings
LP decoder has maximum-likelihood certificate property
Decoding complexity can be reduced with alternative polytopes
Performance comparable to optimal hard-decision decoding in simulations
Abstract
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the 'maximum-likelihood certificate' property. It is also shown that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. It is also proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. Two alternative polytopes for use with linear-programming decoding are studied, and it is shown that for many classes of codes these polytopes yield a complexity advantage for decoding. These…
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