Statistical physics of irregular low-density parity-check codes
نویسندگان
چکیده
منابع مشابه
Design of capacity-approaching irregular low-density parity-check codes
We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the underlying communication channel is symmetric, we prove that the probability densities at the message...
متن کاملImproved low-density parity-check codes using irregular graphs
We construct new families of error-correcting codes based on Gallager’s low-density parity-check codes. We improve on Gallager’s results by introducing irregular parity-check matrices and a new rigorous analysis of hard-decision decoding of these codes. We also provide efficient methods for finding good irregular structures for such decoding algorithms. Our rigorous analysis based on martingale...
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Low Density Parity Check Codes originally invented by Gallagher and subsequently rediscovered by multiple groups 30 years later has become the best known error correcting code in a variety of situations. In this paper, we review regular and irregular LDPC codes. We describe a number of message passing decoders for decoding these codes and explain their operation via examples. Density evolution,...
متن کاملLow-density parity-check codes
A low-density parity-check code is a code specified by a parity-check matrix with the following properties : each column contains a small fixed numberj > 3 of I’s and each row contains a small fixed number k > j of 1’s. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j. When used with maximum likelihood decoding on a snfhciently quiet ...
متن کاملStatistical physics of regular low-density parity-check error-correcting codes
A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword that comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytic...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2000
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/33/37/305