Journal ArticleDOI
Low-density parity check codes over GF(q)
TLDR
A significant improvement over the performance of the binary codes is found, including a rate 1/4 code with bit error probability <10/sup -5/ at E/sub b//N/sub 0/=0.2 dB.Abstract:
Gallager's (1962) low-density binary parity check codes have been shown to have near-Shannon limit performance when decoded using a probabilistic decoding algorithm. We report the empirical results of error-correction using the analogous codes over GF(q) for q>2, with binary symmetric channels and binary Gaussian channels. We find a significant improvement over the performance of the binary codes, including a rate 1/4 code with bit error probability <10/sup -5/ at E/sub b//N/sub 0/=0.2 dB.read more
Citations
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Wireless communications
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Journal ArticleDOI
Good error-correcting codes based on very sparse matrices
TL;DR: It is proved that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit, and experimental results for binary-symmetric channels and Gaussian channels demonstrate that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Journal ArticleDOI
The capacity of low-density parity-check codes under message-passing decoding
TL;DR: The results are based on the observation that the concentration of the performance of the decoder around its average performance, as observed by Luby et al. in the case of a binary-symmetric channel and a binary message-passing algorithm, is a general phenomenon.
Journal ArticleDOI
Regular and irregular progressive edge-growth tanner graphs
TL;DR: Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.
References
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Book
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
Book
Low-Density Parity-Check Codes
TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Journal ArticleDOI
Good error-correcting codes based on very sparse matrices
TL;DR: It is proved that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit, and experimental results for binary-symmetric channels and Gaussian channels demonstrate that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Journal ArticleDOI
Near Shannon limit performance of low density parity check codes
TL;DR: The authors report the empirical performance of Gallager's low density parity check codes on Gaussian channels, showing that performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Good error-correcting codes based on very sparse matrices (vol 45, pg 339, 1999)
TL;DR: It can be proved that, given an optimal decoder, Gallager's low density parity check codes asymptotically approach the Shannon limit.