Pseudo-codeword Landscape
<|reference_start|>Pseudo-codeword Landscape: 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.<|reference_end|>
@article{chertkov2007pseudo-codeword,
    title={Pseudo-codeword Landscape},
    author={Michael Chertkov (Los Alamos) and Mikhail Stepanov (UA, Tucson)},
    journal={arXiv preprint arXiv:cs/0701084},
    year={2007},
    number={LA-UR# 07-0144},
    archivePrefix={arXiv},
    eprint={cs/0701084},
    primaryClass={cs.IT cond-mat.stat-mech math.IT}
}