Low-rank parity-check codes over Galois rings
نویسندگان
چکیده
منابع مشابه
Low density parity check codes over groups and rings
The role of low density parity check principles in the design of group codes for coded modulation is examined. In this context, the structure of linear codes over certain rings Zm and Gm is discussed, and LDPC codes over these ring structures are designed.
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– A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF (q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the th...
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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,...
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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 ...
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| Binary Low Density Parity Check (LDPC) codes have been shown to have near Shannon limit performance when decoded using a probabilis-tic decoding algorithm. The analogous codes deened over nite elds GF (q) of order q > 2 show signii-cantly improved performance. We present the results of Monte Carlo simulations of the decoding of inn-nite LDPC Codes which can be used to obtain good construction...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2020
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-020-00825-9