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Families of LDPC Codes Derived from Nonprimitive BCH Codes and Cyclotomic Cosets
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@MISC{Aly_familiesof,
author = {Salah A. Aly},
title = {Families of LDPC Codes Derived from Nonprimitive BCH Codes and Cyclotomic Cosets},
year = {}
}
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Abstract
Abstract—Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived – one based on nonprimitive narrow-sense BCH codes and the other directly based on cyclotomic cosets. The constructed codes have high rates and are free of cycles of length four; consequently, they can be decoded using standard iterative decoding algorithms. The exact dimension and bounds for the minimum distance and stopping distance are derived. These constructed codes can be used to derive quantum error-correcting codes. Index Terms—LDPC Codes, BCH Codes, Channel Coding, Performance and iterative decoding.
Keyphrases
cyclotomic cosets nonprimitive bch code ldpc code derived important class iterative decoding algebraic method minimum distance quantum error-correcting code many application high rate bch code index term ldpc code exact dimension regular ldpc code abstract low-density parity check constructed code nonprimitive narrow-sense bch code channel coding standard iterative decoding algorithm
