Asymptotic estimation of the fraction of errors correctable by q-ary LDPC codes

We consider an ensemble of random q -ary LDPC codes. As constituent codes, we use q -ary single-parity-check codes with d = 2 and Reed-Solomon codes with d = 3. We propose a hard-decision iterative decoding algorithm with the number of iterations of the order of the logarithm of the code length. We...

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Bibliographic Details
Published in:Problems of information transmission Vol. 46; no. 2; pp. 142 - 159
Main Authors: Frolov, A. A., Zyablov, V. V.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01.06.2010
Subjects:
Coding Theory
Communications Engineering
Control
Electrical Engineering
Engineering
Information Storage and Retrieval
Networks
Systems Theory
Information Transmission
LDPC Code
Asymptotic Estimation
Code Length
Code Rate
ISSN:0032-9460, 1608-3253
Online Access:Get full text
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Summary:We consider an ensemble of random q -ary LDPC codes. As constituent codes, we use q -ary single-parity-check codes with d = 2 and Reed-Solomon codes with d = 3. We propose a hard-decision iterative decoding algorithm with the number of iterations of the order of the logarithm of the code length. We show that under this decoding algorithm there are codes in the ensemble with the number of correctable errors linearly growing with the code length. We weaken a condition on the vertex expansion of the Tanner graph corresponding to the code.
ISSN:0032-9460
1608-3253
DOI:10.1134/S0032946010020043