Construction of Flexible Type II and III QC-LDPC Codes

Gabofetswe Malema; Nkwebi Motlogelwa

doi:doi:10.11648/j.cssp.20140305.11

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Construction of Flexible Type II and III QC-LDPC Codes

Gabofetswe Malema, Nkwebi Motlogelwa

Received: 16 November 2014 Accepted: 21 November 2014 Published: 28 November 2014

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Abstract

Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexible in constructing a wide range (rates and lengths) of type II and III QC-LDPC codes compared to existing methods. Although the proposed algorithm uses a search approach to construct codes, it generally successfully constructs a code even at low code lengths. Constructed codes show better bit error rate performances compared to type I codes as expected.

DOI	10.11648/j.cssp.20140305.11
Published in	Science Journal of Circuits, Systems and Signal Processing (Volume 3, Issue 5, October 2014)
Page(s)	31-34
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

QC-LDPC Codes, Tanner Graph, Girth Code Rate and Length

References

[1]	H. Fujita and K. Sakaniwa, “Some Classes of Quasi-Cyclic LDPC Code: Properties and Efficient Encoding Method”, IEICE Fundamentals,Vol. E88-A, No.12, pp. 3627 – 3635, 2005.
[2]	S. Olcer, “Decoding Architecture for Array-code-based LDPC Codes”, Proc. IEEE GLOBECOM, pp. 2046 – 2050, December 2003.
[3]	L. Chen, J. Xu, I. Djurdjevic, and S. Lin, “Near Shannon-Limit Quasi-Cyclic Low-Density parity-Check Codes,” IEEE Transactions on Communications., vol. 52, pp. 1038–1042, July 2004
[4]	M. O’ Sullivan,J. Brevik and R. Wolski, “The Performance of LDPC Codes with Large Girth,” Proc.of the 43rd Annual Allerton Conference; Communication, Control and Computing, Septem-ber 2005.
[5]	Y. Mao and A. Banihashemi, “A Heuristic Search for Good Low-Density Parity-Check Codes at short Block Lengths,” Proceedings of IEEE International Conference on Communications, Vol. 1, pp,41-44, June 2001.
[6]	R. Smarandache and P.O Vontel, “Quasi-Cyclic LDPC Codes: Influence of Proto and Tanner Graph Structure on minimum Hamming Distance upper Bounds”, IEEE Transactions on Information Theory, 2009.
[7]	B.K Butter and P.H Siegel, “On Distance Properties of Quasi-Cyclic Protograph-Based LDPC Codes”, ISIT 2010, pp. 809 – 813, Austin, Texas, June 13-18, 2010.
[8]	K. Lally, “Explicit Construction of type-II QC LDPC Codes with Girth at least 6”, ISIT2007, pp. 2371 – 2375, Nice, France, June 24-29 2007.
[9]	G. Malema, “Flexible Construction of High-Girth QC-LDPC Codes”, International Journal of Computer Science and Application, Vol. 1 Issue 1 August 2012 pp. 19-25
[10]	G. Malema, “Construction of Type II and III QC-LDPC codes”, http://www.mathworks.de/matlabcentral/fileexchange/authors/30162

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APA Style

Gabofetswe Malema, Nkwebi Motlogelwa. (2014). Construction of Flexible Type II and III QC-LDPC Codes. Science Journal of Circuits, Systems and Signal Processing, 3(5), 31-34. https://doi.org/10.11648/j.cssp.20140305.11

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ACS Style

Gabofetswe Malema; Nkwebi Motlogelwa. Construction of Flexible Type II and III QC-LDPC Codes. Sci. J. Circuits Syst. Signal Process. 2014, 3(5), 31-34. doi: 10.11648/j.cssp.20140305.11

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AMA Style

Gabofetswe Malema, Nkwebi Motlogelwa. Construction of Flexible Type II and III QC-LDPC Codes. Sci J Circuits Syst Signal Process. 2014;3(5):31-34. doi: 10.11648/j.cssp.20140305.11

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@article{10.11648/j.cssp.20140305.11,
  author = {Gabofetswe Malema and Nkwebi Motlogelwa},
  title = {Construction of Flexible Type II and III QC-LDPC Codes},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {3},
  number = {5},
  pages = {31-34},
  doi = {10.11648/j.cssp.20140305.11},
  url = {https://doi.org/10.11648/j.cssp.20140305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20140305.11},
  abstract = {Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexible in constructing a wide range (rates and lengths) of type II and III QC-LDPC codes compared to existing methods. Although the proposed algorithm uses a search approach to construct codes, it generally successfully constructs a code even at low code lengths. Constructed codes show better bit error rate performances compared to type I codes as expected.},
 year = {2014}
}

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TY  - JOUR
T1  - Construction of Flexible Type II and III QC-LDPC Codes
AU  - Gabofetswe Malema
AU  - Nkwebi Motlogelwa
Y1  - 2014/11/28
PY  - 2014
N1  - https://doi.org/10.11648/j.cssp.20140305.11
DO  - 10.11648/j.cssp.20140305.11
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 31
EP  - 34
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20140305.11
AB  - Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexible in constructing a wide range (rates and lengths) of type II and III QC-LDPC codes compared to existing methods. Although the proposed algorithm uses a search approach to construct codes, it generally successfully constructs a code even at low code lengths. Constructed codes show better bit error rate performances compared to type I codes as expected.
VL  - 3
IS  - 5
ER  -

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Author Information

Gabofetswe Malema

Department of Computer Science, University of Botswana, Gaborone, Botswana
Nkwebi Motlogelwa

Department of Computer Science, University of Botswana, Gaborone, Botswana

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APA Style

Gabofetswe Malema, Nkwebi Motlogelwa. (2014). Construction of Flexible Type II and III QC-LDPC Codes. Science Journal of Circuits, Systems and Signal Processing, 3(5), 31-34. https://doi.org/10.11648/j.cssp.20140305.11

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ACS Style

Gabofetswe Malema; Nkwebi Motlogelwa. Construction of Flexible Type II and III QC-LDPC Codes. Sci. J. Circuits Syst. Signal Process. 2014, 3(5), 31-34. doi: 10.11648/j.cssp.20140305.11

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AMA Style

Gabofetswe Malema, Nkwebi Motlogelwa. Construction of Flexible Type II and III QC-LDPC Codes. Sci J Circuits Syst Signal Process. 2014;3(5):31-34. doi: 10.11648/j.cssp.20140305.11

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@article{10.11648/j.cssp.20140305.11,
  author = {Gabofetswe Malema and Nkwebi Motlogelwa},
  title = {Construction of Flexible Type II and III QC-LDPC Codes},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {3},
  number = {5},
  pages = {31-34},
  doi = {10.11648/j.cssp.20140305.11},
  url = {https://doi.org/10.11648/j.cssp.20140305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20140305.11},
  abstract = {Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexible in constructing a wide range (rates and lengths) of type II and III QC-LDPC codes compared to existing methods. Although the proposed algorithm uses a search approach to construct codes, it generally successfully constructs a code even at low code lengths. Constructed codes show better bit error rate performances compared to type I codes as expected.},
 year = {2014}
}

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TY  - JOUR
T1  - Construction of Flexible Type II and III QC-LDPC Codes
AU  - Gabofetswe Malema
AU  - Nkwebi Motlogelwa
Y1  - 2014/11/28
PY  - 2014
N1  - https://doi.org/10.11648/j.cssp.20140305.11
DO  - 10.11648/j.cssp.20140305.11
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 31
EP  - 34
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20140305.11
AB  - Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexible in constructing a wide range (rates and lengths) of type II and III QC-LDPC codes compared to existing methods. Although the proposed algorithm uses a search approach to construct codes, it generally successfully constructs a code even at low code lengths. Constructed codes show better bit error rate performances compared to type I codes as expected.
VL  - 3
IS  - 5
ER  -

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