Searching for low weight pseudo-codewords

TL;DR

This paper investigates the error-floor behavior of LDPC codes under BP and LP decoding by analyzing instantons and pseudo-codewords, introducing optimization algorithms to identify low-weight configurations that dominate error rates.

Contribution

It presents a general optimization method for finding instantons in any coding/decoding scheme and introduces an LP-specific pseudo-codeword search algorithm for efficient spectrum calculation.

Findings

Identified low-weight instantons that dominate error-floor performance.

Developed an efficient algorithm for pseudo-codeword spectrum analysis.

Applied methods to model codes, revealing insights into error-floor behavior.

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.