Absdet-Pseudo-Codewords and Perm-Pseudo-Codewords: Definitions and Properties

TL;DR

This paper introduces absdet-pseudo-codewords and perm-pseudo-codewords, exploring their definitions and properties to enhance understanding of the fundamental cone structure affecting LP decoding performance.

Contribution

It defines new classes of pseudo-codewords and analyzes their properties, contributing to the theoretical understanding of LP decoding in binary linear codes.

Findings

Defined absdet-pseudo-codewords and perm-pseudo-codewords

Discussed properties and examples of these pseudo-codewords

Provided insights into the structure of the fundamental cone

Abstract

The linear-programming decoding performance of a binary linear code crucially depends on the structure of the fundamental cone of the parity-check matrix that describes the code. Towards a better understanding of fundamental cones and the vectors therein, we introduce the notion of absdet-pseudo-codewords and perm-pseudo-codewords: we give the definitions, we discuss some simple examples, and we list some of their properties.