LP decoding excess over symmetric channels

TL;DR

This paper generalizes the LP excess lemma for LP decoding of binary codes from symmetric channels to a broader class of discrete MSB channels, and explores the effect of redundant checks on decoding performance.

Contribution

The paper extends the LP excess lemma to discrete MSB channels and analyzes how redundant checks influence LP decoding in this broader context.

Findings

Generalized LP excess lemma to MSB channels

Extended analysis of redundant checks impact on LP decoding

Provided theoretical framework for broader channel classes

Abstract

We consider the problem of Linear Programming (LP) decoding of binary linear codes. The LP excess lemma was introduced by the first author, B. Ghazi, and R. Urbanke (IEEE Trans. Inf. Th., 2014) as a technique to trade crossover probability for "LP excess" over the Binary Symmetric Channel. We generalize the LP excess lemma to discrete, binary-input, Memoryless, Symmetric and LLR-Bounded (MSB) channels. As an application, we extend a result by the first author and H. Audah (IEEE Trans. Inf. Th., 2015) on the impact of redundant checks on LP decoding to discrete MSB channels.