Low Complexity Encoding Based on Richardson's LDPC Codes

Hyunseuk YOO; Chang Hui CHOE; Moon Ho LEE

doi:10.1093/ietcom/e90-b.8.2151

Low Complexity Encoding Based on Richardson's LDPC Codes

Hyunseuk YOO, Chang Hui CHOE, Moon Ho LEE

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The key weakness of Low-Density Parity Check codes is the complexity of the encoding scheme. The generator matrices can be made by Gaussian elimination of parity check matrices for normal block codes. Richardson succeeded in making parity bits from parity check matrices by the low density computation. In this letter, we focus on the execution of numerical experiments which show that even if the matrix D, which is the part of the Richardson's LDPC matrix, is restricted, proposed LDPC codes is lower complexity than Richardson's LDPC codes. The constraint of D results in reducing complexity from O(n + g²) to O(n) due to the omission of computing inverse matrices of φ and T in Richardson's encoding scheme. All the sub-matrices in parity check matrix are composed of Circulant Permutation Matrices based on Galois Fields.

Publication: IEICE TRANSACTIONS on Communications Vol.E90-B No.8 pp.2151-2154

Publication Date: 2007/08/01

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Online ISSN: 1745-1345

DOI: 10.1093/ietcom/e90-b.8.2151

Type of Manuscript: LETTER

Category: Fundamental Theories for Communications

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Hyunseuk YOO, Chang Hui CHOE, Moon Ho LEE, "Low Complexity Encoding Based on Richardson's LDPC Codes" in IEICE TRANSACTIONS on Communications, vol. E90-B, no. 8, pp. 2151-2154, August 2007, doi: 10.1093/ietcom/e90-b.8.2151.
Abstract: The key weakness of Low-Density Parity Check codes is the complexity of the encoding scheme. The generator matrices can be made by Gaussian elimination of parity check matrices for normal block codes. Richardson succeeded in making parity bits from parity check matrices by the low density computation. In this letter, we focus on the execution of numerical experiments which show that even if the matrix D, which is the part of the Richardson's LDPC matrix, is restricted, proposed LDPC codes is lower complexity than Richardson's LDPC codes. The constraint of D results in reducing complexity from O(n + g²) to O(n) due to the omission of computing inverse matrices of φ and T in Richardson's encoding scheme. All the sub-matrices in parity check matrix are composed of Circulant Permutation Matrices based on Galois Fields.
URL: https://globals.ieice.org/en_transactions/communications/10.1093/ietcom/e90-b.8.2151/_p

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@ARTICLE{e90-b_8_2151,
author={Hyunseuk YOO, Chang Hui CHOE, Moon Ho LEE, },
journal={IEICE TRANSACTIONS on Communications},
title={Low Complexity Encoding Based on Richardson's LDPC Codes},
year={2007},
volume={E90-B},
number={8},
pages={2151-2154},
abstract={The key weakness of Low-Density Parity Check codes is the complexity of the encoding scheme. The generator matrices can be made by Gaussian elimination of parity check matrices for normal block codes. Richardson succeeded in making parity bits from parity check matrices by the low density computation. In this letter, we focus on the execution of numerical experiments which show that even if the matrix D, which is the part of the Richardson's LDPC matrix, is restricted, proposed LDPC codes is lower complexity than Richardson's LDPC codes. The constraint of D results in reducing complexity from O(n + g²) to O(n) due to the omission of computing inverse matrices of φ and T in Richardson's encoding scheme. All the sub-matrices in parity check matrix are composed of Circulant Permutation Matrices based on Galois Fields.},
keywords={},
doi={10.1093/ietcom/e90-b.8.2151},
ISSN={1745-1345},
month={August},}

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TY - JOUR
TI - Low Complexity Encoding Based on Richardson's LDPC Codes
T2 - IEICE TRANSACTIONS on Communications
SP - 2151
EP - 2154
AU - Hyunseuk YOO
AU - Chang Hui CHOE
AU - Moon Ho LEE
PY - 2007
DO - 10.1093/ietcom/e90-b.8.2151
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E90-B
IS - 8
JA - IEICE TRANSACTIONS on Communications
Y1 - August 2007
AB - The key weakness of Low-Density Parity Check codes is the complexity of the encoding scheme. The generator matrices can be made by Gaussian elimination of parity check matrices for normal block codes. Richardson succeeded in making parity bits from parity check matrices by the low density computation. In this letter, we focus on the execution of numerical experiments which show that even if the matrix D, which is the part of the Richardson's LDPC matrix, is restricted, proposed LDPC codes is lower complexity than Richardson's LDPC codes. The constraint of D results in reducing complexity from O(n + g²) to O(n) due to the omission of computing inverse matrices of φ and T in Richardson's encoding scheme. All the sub-matrices in parity check matrix are composed of Circulant Permutation Matrices based on Galois Fields.
ER -