Error floor approximation for LDPC codes in the AWGN channel

Abstract

This paper addresses the prediction of error floors of variable-regular Low Density Parity Check (LDPC) codes in the Additive White Gaussian Noise (AWGN) channel. Specifically, we focus on the Sum-Product Algorithm (SPA) decoder in the log-domain at high SNRs. We hypothesize that several published error floor levels are due to numerical saturation within their decoders when handling high SNRs. We take care to develop a log-domain SPA decoder that does not saturate near-certain messages and find the error rates of our decoder to be lower by at least several orders of magnitude. We study the behavior of near-codewords / trapping sets that dominate the reported error floors.J. Sun, in his Ph.D. thesis, used a linear system model to show that error floors due to elementary trapping sets don't exist under certain conditions, assuming that the SPA decoder is non-saturating [1]. We develop a refined linear model which we find to be capable of predicting the error floors caused by elementary trapping sets for saturating decoders. Performance results of several codes at several levels of decoder saturation are presented.

Performance Bounds and Estimates for Quantized LDPC Decoders

“…In this section, we propose a reduced complexity method to approximate λ(A). Although the term Pr (U = W k ) was eliminated from the expression for Pr(ξ(A)) in (16), thus making the lower bound code-independent and simplifying the expression, calculating λ(A) in (17) still depends on finding Ψ(W ), which, in-turn requires examining all W k ∈ W as shown in (15). In other words, all t κp rows of the decodability array should be examined for each of the t a columns x i .…”

“…Also, [14] and [15] developed a state-space model for a codes dominant absorbing sets to estimate its FER. Later, [16] applied this method to the case where the log-likelihood-ratios (LLRs) used for decoding are constrained to some maximum saturation value. Each of these references considered the problematic structures of a particular code.…”

The l<inf>1</inf> penalized decoder and its reweighted LP

“…We note that the Margulis code is well know for its error floor in the AWGN channel [16]. The "nonsaturating BP" is a robust BP implementation that avoids saturating the log-likelihood ratios of the sum-product BP decoder (see [17] for details), thereby improving decoding performance in the error floor regime. Note that the LPD displays worse performance than BP at low SNRs.…”

Modeling BP decoding error events with the LDPC codes of the DVB-S2 standard

“…Analyzing the error floor is a hard task as extracting analytical equations is near impossible. Very few papers tackle this approach [7], [8]. Three main strategies are followed to fight against the error floor.…”