On Pseudocodewords and Decision Regions of Linear Programming Decoding of HDPC Codes

TL;DR

This paper investigates the decision regions of LP decoding for HDPC codes, compares it with BP and ML decoders, and analyzes the impact of pseudocodewords on decoding performance.

Contribution

It introduces global optimization for finding minimal pseudoweights and provides a complete pseudoweight distribution for the extended Golay code.

Findings

LP decision regions differ from BP and ML regions

Minimal pseudoweights significantly influence LP decoding performance

Pseudoweight distribution alone cannot tightly bound error probability

Abstract

In this paper we explore the decision regions of Linear Programming (LP) decoding. We compare the decision regions of an LP decoder, a Belief Propagation (BP) decoder and the optimal Maximum Likelihood (ML) decoder. We study the effect of minimal-weight pseudocodewords on LP decoding. We present global optimization as a method for finding the minimal pseudoweight of a given code as well as the number of minimal-weight generators. We present a complete pseudoweight distribution for the [24; 12; 8] extended Golay code, and provide justifications of why the pseudoweight distribution alone cannot be used for obtaining a tight upper bound on the error probability.