Pseudo-codeword Landscape
Michael Chertkov (Los Alamos), Mikhail Stepanov (UA, Tucson)

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…
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Taxonomy
TopicsError Correcting Code Techniques · Advanced Wireless Communication Techniques · Optical Network Technologies
