Polytope Representations for Linear-Programming Decoding of Non-Binary Linear Codes

TL;DR

This paper explores various polytope representations for linear-programming decoding of non-binary linear codes, demonstrating that certain polytopes can reduce decoding complexity and enable polynomial-time decoding for many code classes.

Contribution

It introduces new polytope representations that improve decoding efficiency and provide polynomial-time algorithms for a broad range of non-binary codes.

Findings

Polytope representations can reduce decoding complexity.

Certain polytopes enable polynomial-time decoding.

Decoding efficiency varies with polytope choice.

Abstract

In previous work, we demonstrated how decoding of a non-binary linear code could be formulated as a linear-programming problem. In this paper, we study different polytopes for use with linear-programming decoding, and show that for many classes of codes these polytopes yield a complexity advantage for decoding. These representations lead to polynomial-time decoders for a wide variety of classical non-binary linear codes.