Pseudo-codeword Landscape
Chertkov, Michael
Stepanov, Mikhail
Theoretical Division and Center for Nonlinear Studies, LANL, MS B213, T-13, Los Alamos, NM 87545. chertkov@lanl.gov;
This paper appears in: Information Theory, 2007. ISIT 2007. IEEE International Symposium on
Publication Date: 24-29 June 2007
On page(s): 1546-1550
Location: Nice,
ISBN: 978-1-4244-1397-3
Digital Object Identifier: 10.1109/ISIT.2007.4557442
Current Version Published: 2008-07-09
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.
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