---
title: Searching for low weight pseudo-codewords
url: https://www.emergentmind.com/papers/0702024
type: paper
arxiv_id: '0702024'
arxiv_url: https://arxiv.org/abs/0702024
published: '2007-02-04'
categories:
- cs.IT
- math.IT
---

# Searching for low weight pseudo-codewords

## Abstract

Belief Propagation (BP) and Linear Programming (LP) decodings of Low Density Parity Check (LDPC) codes are discussed. We summarize results of instanton/pseudo-codeword approach developed for analysis of the error-floor domain of the codes. Instantons are special, code and decoding specific, configurations of the channel noise contributing most to the Frame-Error-Rate (FER). Instantons are decoded into pseudo-codewords. Instanton/pseudo-codeword with the lowest weight describes the largest Signal-to-Noise-Ratio (SNR) asymptotic of FER, while the whole spectra of the low weight instantons is descriptive of the FER vs SNR profile in the extended error-floor domain. First, we describe a general optimization method that allows to find the instantons for any coding/decoding. Second, we introduce LP-specific pseudo-codeword search algorithm that allows efficient calculations of the pseudo-codeword spectra. Finally, we discuss results of combined BP/LP error-floor exploration experiments for two model codes.