Improving Belief Propagation Decoding of Polar Codes using Bi-Directional Bit-Flipping Strategy
Keywords:polar codes, belief propagation, bit-flipping
It is difficult to achieve high throughput and low latency from the cyclic redundancy check (CRC-) aided successive cancellation list (CA-SCL) polar decoder employed in 5G new radio systems. To tackle this problem, the hardware-efficient belief propagation (BP) decoder has been extensively studied. Unfortunately, the performance of the BP decoding for polar codes is quite poor. To improve the performance of this decoder, a novel bi-directional bit-flipping (BF) strategy is proposed. The rule of generating the flip set based on the post log-likelihood ratio (LLR) is combined with the possibility of the two-way flipping. With the help of this idea, the decoding performance of BP decoder is identical to that of the CA-SCL decoder. Moreover, with the same complexity, our proposed BF strategy outperforms both the best known one-directional BF strategy and the previously found bi-directional BF strategy at BLER of 10-4.
E. Arikan, "Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels," IEEE Transactions on Information Theory, vol. 55, no. 7, 2009, pp. 3051-3073.
S. -N. Hong, D. Hui and I. Marić, "Capacity-Achieving Rate-Compatible Polar Codes," IEEE Transactions on Information Theory, vol. 63, no. 12, 2017, pp. 7620-7632.
E. Arikan, "Channel combining and splitting for cutoff rate improvement," IEEE Transactions on Information Theory, vol. 52, no. 2, 2006, pp. 628-639.
K. Niu and K. Chen, "CRC-Aided Decoding of Polar Codes," IEEE Communications Letters, vol. 16, no. 10, 2012, pp. 1668-1671.
3GPP, "Chairman’s Notes of Agenda Item 7.1.5 Channel coding and modulation, Ad Hoc Chair," document TSG RAN WG1 meeting #87, R1-1613710, Sophia Antipolis, France, Nov. 2016.
A. Balatsoukas-Stimming, P. Giard and A. Burg, "Comparison of Polar Decoders with Existing Low-Density Parity-Check and Turbo Decoders," 2017 IEEE Wireless Communications and Networking Conference Workshops (WCNCW), 2017, pp. 1-6.
Y. Wang et al., "A Low-Latency Successive Cancellation Hybrid Decoder for Convolutional Polar Codes," ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020, pp. 5105-5109.
E. Arikan, "A performance comparison of polar codes and Reed-Muller codes," IEEE Communications Letters, vol. 12, no. 6, 2008, pp. 447-449.
E. Arıkan, "Polar codes : A pipelined implementation", 2010.
N. Hussami, S. B. Korada and R. Urbanke, "Performance of polar codes for channel and source coding," 2009 IEEE International Symposium on Information Theory, 2009, pp. 1488-1492.
A. Pamuk, "An FPGA implementation architecture for decoding of polar codes," 2011 8th International Symposium on Wireless Communication Systems, 2011, pp. 437-441.
Y. Zhang, A. Liu, X. Pan, Z. Ye and C. Gong, "A Modified Belief Propagation Polar Decoder," in IEEE Communications Letters, vol. 18, no. 7, 2014, pp. 1091-1094.
A. Elkelesh, M. Ebada, S. Cammerer and S. ten Brink, "Belief propagation decoding of polar codes on permuted factor graphs," 2018 IEEE Wireless Communications and Networking Conference (WCNC), 2018, pp. 1-6.
K. Niu, K. Chen, J. Lin and Q. T. Zhang, "Polar codes: Primary concepts and practical decoding algorithms," IEEE Communications Magazine, vol. 52, no. 7, 2014, pp. 192-203.
Y. Zhang, Q. Zhang, X. Pan, Z. Ye and C. Gong, "A simplified belief propagation decoder for polar codes," 2014 IEEE International Wireless Symposium (IWS 2014), 2014, pp. 1-4.
B. Yuan and K. K. Parhi, "Early Stopping Criteria for Energy-Efficient Low-Latency Belief-Propagation Polar Code Decoders," IEEE Transactions on Signal Processing, vol. 62, no. 24, 2014, pp. 6496-6506.
S. M. Abbas, Y. Fan, J. Chen and C. Tsui, "High-Throughput and Energy-Efficient Belief Propagation Polar Code Decoder," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 25, no. 3, 2014, pp. 1098-1111,
Y. Yu, Z. Pan, N. Liu and X. You, "Belief Propagation Bit-Flip Decoder for Polar Codes," IEEE Access, vol. 7, 2019, pp. 10937-10946.
Y. Shen, W. Song, Y. Ren, H. Ji, X. You and C. Zhang, "Enhanced Belief Propagation Decoder for 5G Polar Codes With Bit-Flipping," IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 5, 2020, pp. 901-905.
Z. Zhang, K. Qin, L. Zhang, H. Zhang and G. T. Chen, "Progressive Bit-Flipping Decoding of Polar Codes over Layered Critical Sets," GLOBECOM 2017 - 2017 IEEE Global Communications Conference, 2017, pp. 1-6.
Z. Zhang, K. Qin, L. Zhang and G. T. Chen, "Progressive Bit-Flipping Decoding of Polar Codes: A Critical-Set Based Tree Search Approach," IEEE Access, vol. 6, pp. 57738-57750, 2018.
Y. Yongrun, P. Zhiwen, L. Nan and Y. Xiaohu, "Successive Cancellation List Bit-flip Decoder for Polar Codes," 2018 10th International Conference on Wireless Communications and Signal Processing (WCSP), 2018, pp. 1-6.
F. Cheng, A. Liu, Y. Zhang and J. Ren, "Bit-Flip Algorithm for Successive Cancellation List Decoder of Polar Codes," IEEE Access, vol. 7, pp. 58346-58352, 2019.
R. Mori and T. Tanaka, "Performance of Polar Codes with the Construction using Density Evolution," IEEE Communications Letters, vol. 13, no. 7, pp. 519-521, July 2009.
I. Tal and A. Vardy, "How to Construct Polar Codes," IEEE Transactions on Information Theory, vol. 59, no. 10, pp. 6562-6582, Oct. 2013.
P. Trifonov, "Efficient Design and Decoding of Polar Codes," IEEE Transactions on Communications, vol. 60, no. 11, pp. 3221-3227, November 2012.
J. Dai, K. Niu, Z. Si, C. Dong and J. Lin, "Does Gaussian Approximation Work Well for the Long-Length Polar Code Construction?," IEEE Access, vol. 5, pp. 7950-7963, 2017.
Z. Babar et al., "Polar Codes and Their Quantum-Domain Counterparts," IEEE Communications Surveys & Tutorials, vol. 22, no. 1, pp. 123-155, Firstquarter 2020.
J. Zhang and M. Wang, "Belief Propagation Decoder With Multiple Bit-Flipping Sets and Stopping Criteria for Polar Codes," IEEE Access, vol. 8, pp. 83710-83717, 2020.
Y. Shen et al., "Improved Belief Propagation Polar Decoders With Bit-Flipping Algorithms," IEEE Transactions on Communications, vol. 68, no. 11, pp. 6699-6713, Nov. 2020.
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