publication . Doctoral thesis . 2019

Noise-against-Noise Decoders : Low Precision Iterative Decoders

Cochachin Henostroza, Franklin Rafael;
Open Access English
  • Published: 02 May 2019
  • Publisher: HAL CCSD
  • Country: France
Abstract
In this thesis, two improved decoders are defined using quantized input channel with only 3 or 4 bits of precision for low-density parity-check (LDPC) codes. Also, a post-processing algorithm for low precision iterative decoders is proposed. One of the proposed decoders, named Noise- Against-Noise Min-Sum (NAN-MS) decoder, incorporates a certain amount of random perturbation due to deliberate noise injection. The other of the proposed decoders, named Sign- Preserving Min-Sum (SP-MS) decoder, always preserve the sign of the messages and it uses all the possible combinations that can be generated for a given precision. Also, the SP-MS decoder can reduce the precis...
Subjects
free text keywords: Density Evolution, Error correction, LDPC codes, Correction d'erreur, Codes LDPC, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
53 references, page 1 of 4

2 Background 5 2.1 Generalities on LDPC codes . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Ensemble of Regular LDPC codes . . . . . . . . . . . . . . . . . 9 2.1.2 Ensemble of Irregular LDPC codes . . . . . . . . . . . . . . . . 9 2.2 Binary LDPC Decoders . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Message-Passing Decoders . . . . . . . . . . . . . . . . . . . . . 13 2.3 Quantized Min-Sum-Based Decoders and Density Evolution . . . . . . 21 2.3.1 Channel Value Quantization . . . . . . . . . . . . . . . . . . . . 22 2.3.2 Quantized Min-Sum-Based Decoders . . . . . . . . . . . . . . . 24 2.3.3 Density Evolution for Quantized Min-Sum-Based Decoders . . . 26 2.3.4 Asymptotic Bit Error Probability . . . . . . . . . . . . . . . . . 30 2.3.5 Density Evolution threshold . . . . . . . . . . . . . . . . . . . . 31

4 Sign-Preserving Min-Sum Decoders 83 4.1 classical OMS-based Decoders . . . . . . . . . . . . . . . . . . . . . . . 84 4.2 Quantization used for SP-MS Decoders . . . . . . . . . . . . . . . . . . 85 4.3 Sign-Preserving Min-Sum Decoders . . . . . . . . . . . . . . . . . . . . 87 4.4 Optimization of Sign-Preserving Min-Sum Decoders . . . . . . . . . . . 88 4.4.1 Probabilistic Error Model to Optimize SP-MS Decoders . . . . . 89 4.5 Density Evolution for Sign-Preserving Decoders . . . . . . . . . . . . . 91 4.5.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.5.2 DE update for CNU . . . . . . . . . . . . . . . . . . . . . . . . 93 4.5.3 DE update for VNU . . . . . . . . . . . . . . . . . . . . . . . . 93 4.6 Asymptotic Bit Error Probability . . . . . . . . . . . . . . . . . . . . . 94 4.7 Density Evolution threshold . . . . . . . . . . . . . . . . . . . . . . . . 95 4.8 Asymptotic Analysis of Sign-Preserving Min-Sum Decoders . . . . . . . 96 4.8.1 Asymptotic Analysis of SP-MS Decoders for Regular LDPC codes 96 4.8.2 Asymptotic Analysis of SP-MS Decoders for Irregular LDPC codes103 4.9 Finite Length Performance of Sign-Preserving Min-Sum Decoders . . . 105 4.10 Convergence Performance Analysis . . . . . . . . . . . . . . . . . . . . 111 4.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

[12] D. J. C. MacKay and R. M. Neal, “Near shannon limit performance of low density parity check codes,” Electronics Letters, vol. 33, no. 6, pp. 457-458, March 1997.

[13] S.-Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 db of the shannon limit,” IEEE Communications Letters, vol. 5, pp. 58-60, Feb 2001.

[14] J. Chen and M. P. C. Fossorier, “Density evolution for two improved bp-based decoding algorithms of ldpc codes,” IEEE Communications Letters, vol. 6, no. 5, pp. 208-210, May 2002.

[15] J. Chen and M. P. C. Fossorier, “Near optimum universal belief propagation based decoding of low-density parity check codes,” IEEE Transactions on Communications, vol. 50, pp. 406-414, March 2002. [OpenAIRE]

[16] J. Chen, A. Dholakia, E. Eleftheriou, M. P. C. Fossorier, and X.-Y. Hu, “Reducedcomplexity decoding of ldpc codes,” IEEE Transactions on Communications, vol. 53, no. 8, pp. 1288-1299, Aug 2005.

[18] R. Singhal, G. S. Choi, and R. N. Mahapatra, “Quantized ldpc decoder design for binary symmetric channels,” in 2005 IEEE International Symposium on Circuits and Systems, pp. 5782-5785 Vol. 6, May 2005.

[19] J. Zhao, F. Zarkeshvari, and A. H. Banihashemi, “On implementation of min-sum algorithm and its modifications for decoding low-density parity-check (ldpc) codes,” IEEE Transactions on Communications, vol. 53, no. 4, pp. 549-554, April 2005.

[20] V. Savin, “Self-corrected min-sum decoding of ldpc codes,” in 2008 IEEE International Symposium on Information Theory, pp. 146-150, July 2008.

[21] S. K. Planjery, D. Declercq, L. Danjean, and B. Vasic, “Finite alphabet iterative decoders-part i: Decoding beyond belief propagation on the binary symmetric channel,” IEEE Transactions on Communications, vol. 61, pp. 4033-4045, October 2013. [OpenAIRE]

[22] D. Declercq, B. Vasic, S. K. Planjery, and E. Li, “Finite alphabet iterative decoders-part ii: Towards guaranteed error correction of ldpc codes via iterative decoder diversity,” IEEE Transactions on Communications, vol. 61, pp. 4046-4057, October 2013.

[23] T. T. Nguyen-Ly, V. Savin, K. Le, D. Declercq, F. Ghafari, and O. Boncalo, “Analysis and design of cost-efective, high-throughput ldpc decoders,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 26, no. 3, pp. 508-521, March 2018.

[24] T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding ldpc codes,” IEEE Transactions on Communications, vol. 58, pp. 1610-1614, June 2010.

[25] A. Rasheed, P. Ivanis, and B. Vasic, “Fault-tolerant Probabilistic Gradient-Descent Bit Flipping Decoder,” IEEE Communications Letters, vol. Vol. 18, no. 9, pp. 1487- 1490, Sept. 2014. [OpenAIRE]

53 references, page 1 of 4
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Doctoral thesis . 2019

Noise-against-Noise Decoders : Low Precision Iterative Decoders

Cochachin Henostroza, Franklin Rafael;