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

In this paper we develop instanton method introduced in V. Chernyak et al. (2004), M.G. Stepanov et al. (2005) 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