Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH

Ruiyan Du; Qingping Zhou; Fulai Liu; Dong Wang

doi:doi:10.11648/j.sd.20170505.18

| Peer-Reviewed

Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH

Ruiyan Du, Qingping Zhou, Fulai Liu, Dong Wang

Published in Science Discovery (Volume 5, Issue 5)

Received: 13 August 2017 Published: 14 August 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.

Published in	Science Discovery (Volume 5, Issue 5)
DOI	10.11648/j.sd.20170505.18
Page(s)	348-354
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), 2017. Published by Science Publishing Group

Keywords

Protograph LDPC Codes, Quasi-Cyclic Expansion, Short Cycle

References

[1]	E. Prange. Cyclic error-correcting codes in two symbols [J], Air Force Cambridge Res. Center, Cambridge, MA, Tech. Note AFCRC-TN-57-103, 1957.
[2]	P. Elias. Coding for noisy channels [J], IRE Convention Record, 1955, 3(4): 37-46.
[3]	X. Y. Hu, E. Eleftheriou, D. M. Arnold. Progressive edge-growth Tanner graphs [C], Proc. IEEE Global Telecommun. Conf., San Antonio, TX, USA, 2001, 2: 995-1001.
[4]	X. Y. Hu, E. Eleftheriou. D. M. Arnold. Regular and irregular progressive edge-growth tanner graphs [J], IEEE Trans. Inform. Theory, 2005, 51(1): 386-398.
[5]	T. Tian, C. R. Jones, J. D. Villasenor, R. D. Wesel. Selective avoidance of cycles in irregular LDPC code construction [J], IEEE Trans. Commun., 2004, 52(8): 1242-1247.
[6]	Nenad M, Fossorier M P C. Systematic Recursive Construction of LDPC Codes [J]. IEEE. Comm. Lett, 2004, vol.8:302-304.
[7]	Andrews K, Dolinar S, Divsalar D, Jhorpe J. Design of Low-Density Parity-Check(LDPC) Codes for Deep-Space Applications [R]. IPN Progress Report 42-159, 2004, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA,USA
[8]	Thorpe J. Low-Density Parity-Check (LDPC) Codes Constructed from Protographs [R]. IPN Progress Report 42-154, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 2004.
[9]	E. Prange. Cyclic error-correcting codes in two symbols [J], Air Force Cambridge Res. Center, Cambridge, MA, Tech. Note AFCRC-TN-57-103, 1957.
[10]	D. Divsalar, S. Dolinar, and C. Jones. Low-rate LDPC codes with simple protograph structure [C], Proc. IEEE Int. Symp. on Inform. Theory, Adelaide, Australia, 2005, 1622-1626.
[11]	Abbasfar A, Divsalar D, Yao K. Accumulate-Repeat-Accumulate Codes [J]. IEEE Trans. on Communications, 2007, 55(4):692-702.
[12]	R. Asvadi, A. H. Banihashemi, M. Ahmadian-Attari. Design of finite-length irregular protograph codes with low error floors over the binary-input AWGN channel using cyclic liftings [J], IEEE Trans. Commun., 2012, 60(4): 902-907.
[13]	Yige Wang, Stark C. Draper, et al. Hierarchical and High-Girth QC LDPC Codes [J], IEEE Trans. Inform. Theory, 2013, 59(7): 4553-4583.
[14]	Hosung Park, Seokbeom Hong, et al. Design of Multiple-Edge Protographs for QC LDPC Codes Avoiding Short Inevitable Cycles [J], IEEE Trans. Inform. Theory, 2013, 59(7): 4598-4614.
[15]	包建荣，高西奇，刘超，姜斌．扩展原模图ＬＤＰＣ短码的优化构造[J]．华中科技大学学报(自然科学版)，44(5):35-40。
[16]	张昭基，李颖．适用于突发删除信道的非对称空间耦合LDPC码[J]．西安电子科技大学学报(自然科学版)，44(5):1-6。
[17]	T. J. Richardson, R. L. Urbanke, Efficient encoding of low-density parity check codes [J]. IEEE Trans. Commun., Feb. 2001, 47: 808-821.
[18]	刘星成，程浩辉．基于PEG算法的准循环LDPC码构造方法研究[J]．电路与系统学报，8, 2009, 14(4)。

Cite This Article

Plain Text BibTeX RIS

APA Style

Ruiyan Du, Qingping Zhou, Fulai Liu, Dong Wang. (2017). Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH. Science Discovery, 5(5), 348-354. https://doi.org/10.11648/j.sd.20170505.18

Copy | Download

ACS Style

Ruiyan Du; Qingping Zhou; Fulai Liu; Dong Wang. Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH. Sci. Discov. 2017, 5(5), 348-354. doi: 10.11648/j.sd.20170505.18

Copy | Download

AMA Style

Ruiyan Du, Qingping Zhou, Fulai Liu, Dong Wang. Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH. Sci Discov. 2017;5(5):348-354. doi: 10.11648/j.sd.20170505.18

Copy | Download

@article{10.11648/j.sd.20170505.18,
  author = {Ruiyan Du and Qingping Zhou and Fulai Liu and Dong Wang},
  title = {Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH},
  journal = {Science Discovery},
  volume = {5},
  number = {5},
  pages = {348-354},
  doi = {10.11648/j.sd.20170505.18},
  url = {https://doi.org/10.11648/j.sd.20170505.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20170505.18},
  abstract = {One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH
AU  - Ruiyan Du
AU  - Qingping Zhou
AU  - Fulai Liu
AU  - Dong Wang
Y1  - 2017/08/14
PY  - 2017
N1  - https://doi.org/10.11648/j.sd.20170505.18
DO  - 10.11648/j.sd.20170505.18
T2  - Science Discovery
JF  - Science Discovery
JO  - Science Discovery
SP  - 348
EP  - 354
PB  - Science Publishing Group
SN  - 2331-0650
UR  - https://doi.org/10.11648/j.sd.20170505.18
AB  - One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.
VL  - 5
IS  - 5
ER  -

Copy | Download

Author Information

Ruiyan Du

Engineer Optimization & Smart Antenna Institute, Northeastern University at Qinhuangdao, Qinhuangdao, China
Qingping Zhou

Tangshan Normal University, Tangshan, China
Fulai Liu

Engineer Optimization & Smart Antenna Institute, Northeastern University at Qinhuangdao, Qinhuangdao, China
Dong Wang

Shenzhen Transsion Holdings Limited, Shenzhen, China

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Ruiyan Du, Qingping Zhou, Fulai Liu, Dong Wang. (2017). Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH. Science Discovery, 5(5), 348-354. https://doi.org/10.11648/j.sd.20170505.18

Copy | Download

ACS Style

Ruiyan Du; Qingping Zhou; Fulai Liu; Dong Wang. Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH. Sci. Discov. 2017, 5(5), 348-354. doi: 10.11648/j.sd.20170505.18

Copy | Download

AMA Style

Ruiyan Du, Qingping Zhou, Fulai Liu, Dong Wang. Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH. Sci Discov. 2017;5(5):348-354. doi: 10.11648/j.sd.20170505.18

Copy | Download

@article{10.11648/j.sd.20170505.18,
  author = {Ruiyan Du and Qingping Zhou and Fulai Liu and Dong Wang},
  title = {Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH},
  journal = {Science Discovery},
  volume = {5},
  number = {5},
  pages = {348-354},
  doi = {10.11648/j.sd.20170505.18},
  url = {https://doi.org/10.11648/j.sd.20170505.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20170505.18},
  abstract = {One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH
AU  - Ruiyan Du
AU  - Qingping Zhou
AU  - Fulai Liu
AU  - Dong Wang
Y1  - 2017/08/14
PY  - 2017
N1  - https://doi.org/10.11648/j.sd.20170505.18
DO  - 10.11648/j.sd.20170505.18
T2  - Science Discovery
JF  - Science Discovery
JO  - Science Discovery
SP  - 348
EP  - 354
PB  - Science Publishing Group
SN  - 2331-0650
UR  - https://doi.org/10.11648/j.sd.20170505.18
AB  - One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.
VL  - 5
IS  - 5
ER  -

Copy | Download