Searching for low weight pseudo-codewords
<|reference_start|>Searching for low weight pseudo-codewords: Belief Propagation (BP) and Linear Programming (LP) decodings of Low Density Parity Check (LDPC) codes are discussed. We summarize results of instanton/pseudo-codeword approach developed for analysis of the error-floor domain of the codes. Instantons are special, code and decoding specific, configurations of the channel noise contributing most to the Frame-Error-Rate (FER). Instantons are decoded into pseudo-codewords. Instanton/pseudo-codeword with the lowest weight describes the largest Signal-to-Noise-Ratio (SNR) asymptotic of FER, while the whole spectra of the low weight instantons is descriptive of the FER vs SNR profile in the extended error-floor domain. First, we describe a general optimization method that allows to find the instantons for any coding/decoding. Second, we introduce LP-specific pseudo-codeword search algorithm that allows efficient calculations of the pseudo-codeword spectra. Finally, we discuss results of combined BP/LP error-floor exploration experiments for two model codes.<|reference_end|>
@article{chertkov2007searching,
    title={Searching for low weight pseudo-codewords},
    author={M. Chertkov (Los Alamos), M. Stepanov (UA, Tucson)},
    journal={arXiv preprint arXiv:cs/0702024},
    year={2007},
    number={LA-UR # 07-0509},
    archivePrefix={arXiv},
    eprint={cs/0702024},
    primaryClass={cs.IT math.IT}
}