Some Classes of Quasi-Cyclic LDPC Codes: Properties and Efficient Encoding Method

Hachiro FUJITA; Kohichi SAKANIWA

doi:10.1093/ietfec/e88-a.12.3627

Some Classes of Quasi-Cyclic LDPC Codes: Properties and Efficient Encoding Method

Hachiro FUJITA, Kohichi SAKANIWA

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Low-density parity-check (LDPC) codes are one of the most promising next-generation error-correcting codes. For practical use, efficient methods for encoding of LDPC codes are needed and have to be studied. However, it seems that no general encoding methods suitable for hardware implementation have been proposed so far and for randomly constructed LDPC codes there have been no other methods than the simple one using generator matrices. In this paper we show that some classes of quasi-cyclic LDPC codes based on circulant permutation matrices, specifically LDPC codes based on array codes and a special class of Sridhara-Fuja-Tanner codes and Fossorier codes can be encoded by division circuits as cyclic codes, which are very easy to implement. We also show some properties of these codes.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.12 pp.3627-3635

Publication Date: 2005/12/01

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DOI: 10.1093/ietfec/e88-a.12.3627

Type of Manuscript: PAPER

Category: Coding Theory

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Hachiro FUJITA, Kohichi SAKANIWA, "Some Classes of Quasi-Cyclic LDPC Codes: Properties and Efficient Encoding Method" in IEICE TRANSACTIONS on Fundamentals, vol. E88-A, no. 12, pp. 3627-3635, December 2005, doi: 10.1093/ietfec/e88-a.12.3627.
Abstract: Low-density parity-check (LDPC) codes are one of the most promising next-generation error-correcting codes. For practical use, efficient methods for encoding of LDPC codes are needed and have to be studied. However, it seems that no general encoding methods suitable for hardware implementation have been proposed so far and for randomly constructed LDPC codes there have been no other methods than the simple one using generator matrices. In this paper we show that some classes of quasi-cyclic LDPC codes based on circulant permutation matrices, specifically LDPC codes based on array codes and a special class of Sridhara-Fuja-Tanner codes and Fossorier codes can be encoded by division circuits as cyclic codes, which are very easy to implement. We also show some properties of these codes.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.12.3627/_p

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@ARTICLE{e88-a_12_3627,
author={Hachiro FUJITA, Kohichi SAKANIWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Some Classes of Quasi-Cyclic LDPC Codes: Properties and Efficient Encoding Method},
year={2005},
volume={E88-A},
number={12},
pages={3627-3635},
abstract={Low-density parity-check (LDPC) codes are one of the most promising next-generation error-correcting codes. For practical use, efficient methods for encoding of LDPC codes are needed and have to be studied. However, it seems that no general encoding methods suitable for hardware implementation have been proposed so far and for randomly constructed LDPC codes there have been no other methods than the simple one using generator matrices. In this paper we show that some classes of quasi-cyclic LDPC codes based on circulant permutation matrices, specifically LDPC codes based on array codes and a special class of Sridhara-Fuja-Tanner codes and Fossorier codes can be encoded by division circuits as cyclic codes, which are very easy to implement. We also show some properties of these codes.},
keywords={},
doi={10.1093/ietfec/e88-a.12.3627},
ISSN={},
month={December},}

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TY - JOUR
TI - Some Classes of Quasi-Cyclic LDPC Codes: Properties and Efficient Encoding Method
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3627
EP - 3635
AU - Hachiro FUJITA
AU - Kohichi SAKANIWA
PY - 2005
DO - 10.1093/ietfec/e88-a.12.3627
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2005
AB - Low-density parity-check (LDPC) codes are one of the most promising next-generation error-correcting codes. For practical use, efficient methods for encoding of LDPC codes are needed and have to be studied. However, it seems that no general encoding methods suitable for hardware implementation have been proposed so far and for randomly constructed LDPC codes there have been no other methods than the simple one using generator matrices. In this paper we show that some classes of quasi-cyclic LDPC codes based on circulant permutation matrices, specifically LDPC codes based on array codes and a special class of Sridhara-Fuja-Tanner codes and Fossorier codes can be encoded by division circuits as cyclic codes, which are very easy to implement. We also show some properties of these codes.
ER -