Modified augmented belief propagation for general memoryless channels

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(1)Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 18833. To link to this article : DOI : 10.1109/ISTC.2016.7593103 URL : http://dx.doi.org/10.1109/ISTC.2016.7593103. To cite this version : Gadat, Benjamin and Poulliat, Charly Modified augmented belief propagation for general memoryless channels. (2016) In: 9th International Symposium on Turbo Codes and Iterative Information Processing (ISTC 2016), 5 September 2016 - 9 September 2016 (Brest, France).. Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr.

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(30) 2016 9th International Symposium on Turbo Codes & Iterative Information Processing. Fig. 6. Fig. 4.. Comparison of node selection for R = {2/ 3, 4/ 5} SeiRA codes. -+- BP ~ ABP- A i g _ B - 6 1 ayers. '". _.,_ OABP - 6 1ayers ~ OABP- 11 1 ayers. -. ABP- Aig.B - ll layers. ~ ABP- Alg. A - 111ayers. -. ML deceder. OABP versus BP on the BSC channel for the Tanner code.. the augmented decoding procedure based on a pruning of the branching tree used for the sequential decoding schedule with decoder reinitialization. The proposed algorithm shows near ML decoding performance while decreasing the overall complexity of the original algorithm. Moreover complexityperformance trade-off is an built-in feature for this kind of algorithm. Future works will consider the application to more general message passing algorithms. REFERENCES [!]. M. Fossorier, "Iterative reliability-based decoding of low-density parity check codes," IEEE J. on Sel. Areas in Comm., vol. 19, no. 5, pp. 908- 917, May 2001.. [2]. N. Varnica, M. Fossorier, and A. Kavcic, "Augmented belief propagation decoding of low-density parity check codes," IEEE Trans. on Comm., vol. 55, no. 7, pp. 1308- 1317, July 2007.. [3]. N. Varnica and M. Fossorier, "lmprovements in belief-propagation decoding based on averaging information from decoder and correction of clusters of nodes," IEEE Comm. Letters, vol. 10, no. 12, pp. 846-848, Dec. 2006. H. Pishro-Nik and H. Fekri , "Improved decoding algorithms for lowdensity parity-check codes," in !nt. Corif. Turbo Codes Re/at. Top. , Brest, France, 2003.. .~.L_--~--~--~~--~ , ---7~--~--~--~ Eb/No. Fig. 5.. Comparison of ABP algorithm A and B from [2] for Tanner code. [4]. of our OABP on the BSC with the classical BP decoder. It can be also compared to the results of the FAID decoder with decoder diversity (9239 FAID decoders) in [13]. As a proof of concept, to show that ML performance can be achieved, we set L 0 = 1000 and additional number of iterations is also set to L = 1000 with 11 layers. The curves shown in Fig. 6 are very close to the ML bound given in [13] but with a lower complexity than the FAID decoder diversity using 9239 decoders. The same behavior is observed for the N = 2640 R = 1/2 Margulis code as shown in Fig. 6. The number of iterations is set to 100 with 10 additional iterations.. VI.. [5]. C. Measson, A. Montanari , and R. Urbanke, "Maxwell construction: The hidden bridge between iterative and maximum a posteriori decoding," IEEE Trans. on Tnf Theory, vol. 54, no. 12, pp. 5277- 5307, Dec 2008.. [6]. J. Kang, Q. Huang, S. Lin , and K. Abdel-Ghaffar, "An iterative decoding algorithm with backtracking to lower the error-floors of LDPC codes," IEEE Trans. on Comm., vol. 59, no. l , pp. 64- 73, Jan. 2011.. [7]. W. Ryan and S. Lin, Channel Codes: Classical and Modem . Cambridge University Press, 2009. R. Tanner, "A recursive approach to low complexity codes," IEEE Trans. on !nf The01y, vol. 27, no. 5, pp. 533- 547, Sep 1981.. [8] [9]. S. Gounai and T. Ohtsuki , " Decoding algorithms based on oscillation for low-density parity check codes," fElCE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, vol. E88-A, no. 8, pp. 2216-2226, August 2005.. [10]. M. Zhou and X. Gao, "lmproved augmented belief propagation decoding based on oscillation," in A.-P. Conf on Comm. , Oct. 2008, pp. 1-4.. [Il]. S. Gounai, T. Ohtsuki, and T. Kaneko, "Modified belief propagation decoding algorithm for low-density parity check code based on oscillation," in IEEE VTC, vol. 3, May 2006, pp. 1467- 1471.. [12]. G. Lechner, "Convergence of sum-product algorithm for finite length low-density parity-check codes;' in Winter School on Coding and Tnf Theory, Ascona, Switzerland , February 2003.. [13]. D. Declercq, E. Li , B. Yasic, and S. Planjery, "Approaching maximum likelihood decoding of finite length LDPC codes via FAID diversity," in IEEE ITW, Sept 2012, pp. 487-491.. CONCLUSION. In this paper, we have proposed an efficient implementation of the augmented belief propagation algorithm for LDPC codes over general memoryless channels. Compared to the original implementation, we have considered a different approach for both steps. First, we have shown that a good choice for the node selection is to track the dynarnic of sign changes of the extrinsic messages at the output of the variable nodes. This enables us to consider indifferently general memoryless channels, such as the BSC or the AWGN channel, while still taking into account the influence of irregularity in the graph connectivity. Then, we propose a simple yet efficient implementation of 195.

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