Instanton analysis of Low-Density-Parity-Check codes in the error-floor regime

TL;DR

This paper applies the instanton method to analyze the error-floor performance of LDPC codes, providing a quantitative approach that compares favorably with Monte Carlo simulations in moderate SNR regimes.

Contribution

It introduces a detailed instanton-amoeba scheme for LDPC performance analysis and compares two regular LDPC codes, enhancing understanding of error-floor phenomena.

Findings

Instanton-amoeba scheme effectively predicts error-floor performance.

Comparison shows good agreement with Monte Carlo simulations.

Analysis highlights differences between Tanner and Margulis codes.

Abstract

In this paper we develop instanton method introduced in [1], [2], [3] to analyze quantitatively performance of Low-Density-Parity-Check (LDPC) codes decoded iteratively in the so-called error-floor regime. We discuss statistical properties of the numerical instanton-amoeba scheme focusing on detailed analysis and comparison of two regular LDPC codes: Tanner's (155, 64, 20) and Margulis' (672, 336, 16) codes. In the regime of moderate values of the signal-to-noise ratio we critically compare results of the instanton-amoeba evaluations against the standard Monte-Carlo calculations of the Frame-Error-Rate.