Reducing the Complexity of the Linear Programming Decoding

TL;DR

This paper presents a method to significantly reduce the complexity of linear programming decoding by modeling check equations with degree 3, decreasing constraints from exponential to linear in number.

Contribution

The authors introduce a novel approach that models all check degrees with degree 3 equations, reducing the LP decoding constraints from exponential to linear complexity.

Findings

Constraint count reduced from O(n*2^n) to O(n)

Decoding complexity decreases significantly

Method maintains decoding performance

Abstract

In this paper we show how the complexity of Linear Programming (LP) decoder can decrease. We use the degree 3 check equation to model all variation check degrees. The complexity of LP decoding is directed relative to the number of constraint. Number of constraint for original LP decoder is O(n*(2^n)). Our method decrease the number of the constraint to O(n).