Introduction to Mathematical Programming-Based Error-Correction Decoding

TL;DR

This paper introduces the use of mathematical programming, especially linear programming, for decoding error-correcting codes, highlighting recent advances that make practical applications feasible and bridging optimization with coding theory.

Contribution

It provides an in-depth introduction to mathematical optimization in decoding and reviews recent research connecting optimization techniques with coding theory.

Findings

LP decoding is a viable alternative to algebraic and iterative methods

Recent research has advanced the practical application of LP decoding

The paper bridges mathematical optimization and coding theory

Abstract

Decoding error-correctiong codes by methods of mathematical optimization, most importantly linear programming, has become an important alternative approach to both algebraic and iterative decoding methods since its introduction by Feldman et al. At first celebrated mainly for its analytical powers, real-world applications of LP decoding are now within reach thanks to most recent research. This document gives an elaborate introduction into both mathematical optimization and coding theory as well as a review of the contributions by which these two areas have found common ground.