Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

TL;DR

This paper reviews how mathematical programming techniques like linear and integer programming are used to develop new decoding algorithms for binary linear codes, offering alternatives to traditional iterative methods.

Contribution

It categorizes and analyzes various decoding methods based on mathematical programming, highlighting their theoretical foundations and potential advantages.

Findings

Mathematical programming provides a rigorous framework for decoding.

Decoding methods based on programming can outperform heuristic algorithms.

The survey identifies key mathematical concepts underpinning these decoding strategies.

Abstract

Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory. This survey article reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels.