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A New PWL Approximation for the “Self-Adjustable Offset Min-Sum” Decoding with a highly Reduced-Complexity

International Journal of Computer Applications
© 2013 by IJCA Journal
Volume 61 - Number 19
Year of Publication: 2013
Abdessalam Ait Madi
Anas Mansouri
Ali Ahaitouf

Abdessalam Ait Madi, Anas Mansouri and Ali Ahaitouf. Article: A New PWL Approximation for the "Self-Adjustable Offset Min-Sum" Decoding with a highly Reduced-Complexity. International Journal of Computer Applications 61(19):1-6, January 2013. Full text available. BibTeX

	author = {Abdessalam Ait Madi and Anas Mansouri and Ali Ahaitouf},
	title = {Article: A New PWL Approximation for the "Self-Adjustable Offset Min-Sum" Decoding with a highly Reduced-Complexity},
	journal = {International Journal of Computer Applications},
	year = {2013},
	volume = {61},
	number = {19},
	pages = {1-6},
	month = {January},
	note = {Full text available}


A new PieceWiseLinear (PWL) function is proposed for the decoding of the Low-Density-Parity-Check (LDPC) code with the Self Adjustable Offset Min-Sum (SAOMS) algorithm. Avoiding the use of the non-linear function f(x) = ln ?? 1 + e??jxj in the adjustable offset factor, this linear approximation greatly simplifies the hardware implementation with a little BER performance loss. The proposed solution is new, useful and is successfully tested on decoding regulars (504, 252) and (8000, 4000) LDPC codes. The corresponding Check Node Processing Unit (CNPU) have been designed, described and simulated using Very High Speed integrated circuits Hardware Description language(VHDL). The synthesis results were obtained using an Altera Quartus II software with cyclone II EP2CF896C6 as the target FPGA device. The designed CNPU is fully parallel and flexible to be used for different block length when a regulars (3, 6) LDPC codes are required.


  • Digital Video Broadcasting (DVB). 2004. Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications. Draft ETSI EN 302 307 V1. 1, European Standard (Telecommunications series).
  • Digital Video Broadcasting (DVB). 2009. frame structure, channel coding and modulation systems for second generation digital terrestriel television broadcasting system (DVBT2). Draft ETSI EN 302 755 V1. 1. 1 , European Standard (Telecommunications series).
  • R. G. Gallager. 1963. Low Density Parity Check Codes. MA: MIT Press. Cambridge.
  • D. J. C. Mackay. Good Error-Correcting Codes Based on very Sparse Matrices. IEEE Transaction on information Theory. Res. 45(Jan. 1999), 399-431.
  • M. P. C. Fossorier,M. Mihaljevic,H. Imai. Reduced Complexity Iterative Decoding of Low Density Parity Check codes based on Belief Propagation. IEEE Transaction on Communications. 47(May. 1999), 673-680.
  • J. Chen,A. Dholakia,E. Eleftheriou,M. Fossorier,X. Y. Hu. Reduced-Complexity Decoding of LDPC codes. IEEE Transaction On Communications. 53(Aug. 2005), 1288-1299.
  • J. Chen, M. P. C. Fossorier. 2003. Density evolution for BPbased decoding algorithms of LDPC codes and their quantized versions. In Proceedings of the IEEE GlOBCOM'02.
  • S. L. Howard, C. Schlegel, and V. C. Gaudet. Degreematched check node decoding for regular and irregular LDPCs. IEEE Transaction on Circuits and Systems II: Express Briefs. 53(Oct. 2006), 1054-1058.
  • M. Jiang, C. Zhao, L. Zhang, and E. Xu. Adaptive offset min-sum algorithm for low-density parity check codes. IEEE Communications Letters, 10(2006), 483-485.
  • W. Ji,M. Hamaminto,H. Nakayam,S. Goto. Self-Adjustable Offset min-sum Algorithm for ISDB-S2 LDPC Decoder. IEICE Electronis Express. 7(Aug. 2010), 1283-1289
  • M. M. Mansour,N. R. Shanbhag. High-Throughput LDPC Decoders. IEEE Transaction on very large integration systems. 11(Dec. 2003), 976-996.
  • X. Yu. Hu, E. Eleftheriou, D. M. Arnold, A. Dholakia. 2002. Efficient Implementation of the Sum-Product Algorithm for Decoding LDPC Codes. In Proceedings of the IEEE GlOBCOM' 01.
  • R. M. Tanner. A recursive Approach to Low Complexity Codes. IEEE Transaction on information Theory. IT-27(Sep. 1981), 533-547
  • D. J. C. MacKay, Online database of low-density paritycheck codes,http:// www. inference. phy. cam. ac. uk/mackay/ CodesFiles. html