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Computer Science > Information Theory

arXiv:cs/0701084 (cs)
[Submitted on 12 Jan 2007 (v1), last revised 22 Apr 2007 (this version, v2)]

Title:Pseudo-codeword Landscape

Authors:Michael Chertkov (Los Alamos), Mikhail Stepanov (UA, Tucson)
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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.
Comments: 5 pages, 2 figures, proceedings of ISIT '07
Subjects: Information Theory (cs.IT); Statistical Mechanics (cond-mat.stat-mech)
Report number: LA-UR# 07-0144
Cite as: arXiv:cs/0701084 [cs.IT]
  (or arXiv:cs/0701084v2 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.cs/0701084

Submission history

From: Michael Chertkov [view email]
[v1] Fri, 12 Jan 2007 23:17:17 UTC (57 KB)
[v2] Sun, 22 Apr 2007 05:22:40 UTC (57 KB)
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