Pseudo-codeword Landscape

TL;DR

This paper analyzes the performance of LDPC codes decoded by LP at high SNRs, introducing a new method to reduce complexity and examining the influence of pseudo-codewords on error rates.

Contribution

It presents a novel 'dendro' trick to simplify LP decoding and explores the relationship between pseudo-codeword spectra and decoding performance regimes.

Findings

Dendro-code performs similarly to high-connectivity codes under MAP decoding.

Error floors or transient regimes are observed depending on pseudo-codeword spectra.

The method enables detailed analysis of FER dependence on SNR for LDPC codes.

Abstract

We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Programming (LP) at moderate and large Signal-to-Noise-Ratios (SNR). Utilizing a combination of the previously introduced pseudo-codeword-search method and a new "dendro" trick, which allows us to reduce the complexity of the LP decoding, we analyze the dependence of the Frame-Error-Rate (FER) on the SNR. Under Maximum-A-Posteriori (MAP) decoding the dendro-code, having only checks with connectivity degree three, performs identically to its original code with high-connectivity checks. For a number of popular LDPC codes performing over the Additive-White-Gaussian-Noise (AWGN) channel we found that either an error-floor sets at a relatively low SNR, or otherwise a transient asymptote, characterized by a faster decay of FER with the SNR increase, precedes the error-floor asymptote. We explain these regimes in terms of the pseudo-codeword spectra of the codes.