可分解的可分组设计构造的LDPC码

doi:10.3969/j.issn.1001-2400.2017.03.006

Abstract

Abstract:

A new construction method for low-density parity-check (LDPC) codes is presented based on resolvable group divisible designs (RGDDs). The resulting LDPC codes are free of 4-cycle. With the use of RGDDs, a class of masking matrices is also constructed, and then many more quasi-cyclic (QC) LDPC codes are obtained by the masking technique. Numerical results show that the proposed LDPC codes with iterative decoding using the sum-product algorithm perform very well over the AWGN channel. Furthermore, the QC-LDPC codes constructed based on masking have a better BER/FER performance than the original ones.

Key words: LDPC codes, girth, masking, resolvable group divisible designs

SUN Cheng;XU Hengzhou;FENG Dan;BAI Baoming;ZHANG Yulong. LDPC codes constructed from resolvable group divisible designs[J].Journal of Xidian University, 2017, 44(3): 31-35+42.

References

［1］ GALLAGER R G. Low-density Parity-check Codes ［J］. IRE Transactions on Information Theory, 1962, 8(1): 21-28.
［2］ MACKAY D J C, NEAL R M. Near Shannon Limit Performance of Low Density Parity check Codes ［J］. Electronics Letters, 1996, 32(18): 1645-1646.
［3］ WANG R, LI Y, ZHAO H, et al. Construction of Girth-eight Quasi-cyclic Low-density Parity-check Codes with Low Encoding Complexity ［J］. IET Communications, 2016, 10(2): 148-153.
［4］ BABAR Z, BOTSINIS P, ALANIS D, et al. Construction of Quantum LDPC Codes from Classical Row-circulant QC-LDPCs［J］. IEEE Communications Letters, 2016, 20(1): 9-12.
［5］ LEE J H, SUNWOO M H. Low-complexity First-two-minimum-values Generator for Bit-serial LDPC Decoding ［J］. IEEE Transactions on Circuits and Systems II: Express Briefs, 2016, 63(5):483-487.
［6］ OLMOS P M, MITCHELL D G M, COSTELLO D J. Analyzing the Finite-length Performance of Generalized LDPC Codes ［C］//Preceedings of the IEEE International Symposium on Information Theory. Piscataway: IEEE, 2015: 2083-2687.
［7］ FANG Y, BI G, GUAN Y L, et al. A Survey on Protograph LDPC Codes and Their Applications ［J］. IEEE Communications Surveys and Tutorials, 2015, 17(4): 1989-2016.
［8］ DIAO Q, TAI Y Y, LIN S, et al. LDPC Codes on Partial Geometries: Construction, Trapping Set Structure, and Puncturing ［J］. IEEE Transactions on Information Theory, 2013, 59(12): 7898-7914.
［9］ LAN L, TAI Y Y, LIN S, et al. New Constructions of Quasi-cyclic LDPC Codes Based on Special Classes of BIBDs for the AWGN and Binary Erasure Channels ［J］. IEEE Transactions on Communications, 2008, 56(1):39-48.
［10］ SONG S, ZHOU B, LIN S, et al. A Unified Approach to the Construction of Binary and Nonbinary Quasi-cyclic LDPC Codes Based on Finite Fields ［J］. IEEE Transactions on Communications, 2009, 57(1), 84-93.
［11］ LI J, LIU K, LIN S, et al. A Matrix-theoretic Approach to the Construction of Non-binary Quasi-cyclic LDPC Codes ［J］. IEEE Transactions on Communications, 2015, 63(4): 1057-1068.
［12］ VASIC B, MILENKOVIC O. Combinatorial Constructions of Low-density Parity-check Codes for Iterative Decoding ［J］. IEEE Transactions on Information Theory, 2004, 50(6): 1156-1176.
［13］ CHEN C, BAI B M, WANG X M. Construction of Nonbinary Quasi-cyclic LDPC Cycle Codes Based on Singer Perfect Difference Set ［J］. IEEE Communications Letters, 2010, 14(2): 181-183.
［14］ RYAN W E, LIN S. Channel Codes: Classical and Modern ［M］. Cambridge: Cambridge University Press, 2009: 487-490.
［15］ XU H Z, FENG D, SUN C, et al. Construction of LDPC Codes Based on Resolvable Group Divisible Designs ［C］//Preceedings of the 2015 International Workshop on High Mobility Wireless Communications. Piscataway: IEEE, 2015: 111-115.
［16］沈灏. 组合设计理论［M］. 2版. 上海: 上海交通大学出版社, 2008: 16-18.
［17］ SUN X W, GE G N. Resolvable Group Divisible Designs with Block Size Four and General Index ［J］. Discrete Mathematics, 2009, 309(10): 2982-2989.
［18］ MACKAY D. MacKay 's Homepage ［DB/OL］. ［2015-10-26］. http://www.inference.phy.cam.ac.uk/mackay/CodesFiles.html.
［19］ XU J, CHEN L, DJURDJEVIC I, et al. Construction of Regular and Irregular LDPC Codes: Geometry Decomposition and Masking ［J］. IEEE Transactions on Information Theory, 2007, 53(1): 121-134.

[1]	ZHOU Shenyang,BAI Baoming,REN Zhaofeng,ZHU Min,LI Binghao,TANG Ruibo. Study on belief propagation list decoding of concatenated polar codes with high throughput [J]. Journal of Xidian University, 2020, 47(6): 58-65.
[2]	SUN Yue,LI Beilei,LIANG Caihong,LI Ying. Design of serial connecting multiple spatially coupled LDPC codes for block-fading channels [J]. Journal of Xidian University, 2019, 46(2): 1-5.
[3]	XU Hengzhou;SUN Cheng;BAI Baoming. Nonbinary LDPC codes constructed based on cyclic difference families [J]. Journal of Xidian University, 2017, 44(1): 6-11+28.
[4]	LIU Yang;LI Jing'e;LI Ying. Design of bilayer lengthened LDPC codes for decode-and-forward in relay channels [J]. J4, 2014, 41(5): 13-17.
[5]	LIN Wei;BAI Baoming;WANG Xuepeng. Dynamic extended mim-sum decoding algorithm for Q-ary LDPC codes [J]. J4, 2012, 39(2): 59-65.
[6]	XIAO Heling;CAI Ning;WANG Xiao. Application of quantum LDPC codes to quantum key distribution [J]. J4, 2012, 39(2): 8-11+23.
[7]	HE Guanghua;BAI Baoming;LI Bo;LIN Wei. FPGA implementation of a non-binary LDPC decoder using the EMS algorithm [J]. J4, 2011, 38(5): 27-33.
[8]	ZHANG Guohua；WANG Xinmei. On the existence of a class of QC-LDPC codes with girth at least six [J]. J4, 2011, 38(3): 136-139+149.
[9]	HU Shukai;WANG Xinmei. Simplified decoding algorithm for LDPC over GF(q) [J]. J4, 2011, 38(2): 8-12+196.
[10]	ZHOU Lin;BAI Baoming;SHAO Junhu;LIN Wei. On nonbinary rate-compatible LDPC codes [J]. J4, 2011, 38(1): 147-152.
[11]	CUI Jun-yun;BAI Bao-ming;GUO Xu-dong. Improved cycle elimination algorithm for construction of QC-LDPC codes [J]. J4, 2010, 37(4): 700-704.
[12]	HU Jia-yi;WANG Wen-bo. Algorithm for constructing QC_LDPC codes based on the weighted map [J]. J4, 2008, 35(5): 938-941.
[13]	WU Xiao-li1;2;GE Jian-hua1;WANG Yong1. Performance of non-binary concatenated coded OFDM systems [J]. J4, 2008, 35(3): 459-463.
[14]	WANG Dan;TONG Sheng;LI Ying;WANG Xin-mei. A fast convergence decoding algorithm for LDPC codes [J]. J4, 2005, 32(1): 103-107.
[15]	CHEN Dan;WU Qian-hong;WANG Yu-min. A robust watermarking authentication algorithm using the value of visual masking [J]. J4, 2004, 31(6): 929-933.

LDPC codes constructed from resolvable group divisible designs

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10