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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Reduced-Complexity Belief Propagation Decoding for Polar Codes

Jung-Hyun Kim, Inseon Kim, Gangsan Kim, Hong‐Yeop Song

Published Jan 1, 2017• 2 citations
Publisher

Abstract

We propose three effective approximate belief propagation decoders for polar codes using Maclaurin's series, piecewise linear function, and stepwise linear function. The proposed decoders have the better performance than that of existing approximate belief propagation polar decoders, min-sum decoder and normalized min-sum decoder, and almost the same performance with that of original belief propagation decoder. Moreover, the proposed decoders achieve such performance without any optimization process according to the code parameters and channel condition unlike normalized min-sum decoder, offset min-sum decoder, and their variants.

DOI
10.1587/transfun.e100.a.2052

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arXiv:1504.06025•Apr 23, 2015•2 citations
We propose three effective approximate belief propagation decoders for polar codes using Maclaurin's series, piecewise linear function, and stepwise linear function. The proposed decoders have the better performance than that of existing approximate belief propagation polar decoders, min-sum decoder and normalized min-sum decoder, and almost the same performance with that of original belief propagation decoder. Moreover, the proposed decoders achieve such performance without any optimization process according to the code parameters and channel condition unlike normalized min-sum decoder, offset min-sum decoder, and their variants.
In 2009, the presentation of polar code, the first theory to approach the Shannon limit of communication channel coding schemes. Thus, academics and business have focused on Polar codes. Research and worldwide standards have been offered one after another, establishing the groundwork for its real-world use.The paper proposes a min-sum decoding technique for enhanced Polar codes and revises the node update formula in the min-sum decoding algorithm by using the piecewise linear function to approximate the function ln cosh(x) in the belief propagation decoding algorithm. Compared to the min-sum decoding algorithm, the enhanced approach improves decoding performance while somewhat increasing complexity. Compared to the belief propagation decoding algorithm, this approach decreases computational complexity significantly and is simpler to implement in hardware. Based on the min-sum method and the belief propagation algorithm, this approach is offered as a balance between complexity and performance. The simulation results demonstrate that the enhanced min-sum decoding algorithm performs similarly to its predecessor. The performance of the degree propagation decoding method is almost identical to that of the min-sum decoding technique, which is superior.
This paper presents deep learning (DL) methods to optimize polar belief propagation (BP) decoding and concatenated LDPC-polar codes. First, two-dimensional offset Min-Sum (2-D OMS) decoding is proposed to improve the error-correction performance of existing normalized Min-Sum (NMS) decoding. Two optimization methods used in DL, namely back-propagation and stochastic gradient descent, are exploited to derive the parameters of proposed algorithms. Numerical results demonstrate that there is no performance gap between 2-D OMS and exact BP on various code lengths. Then the concatenated OMS algorithms with low complexity are presented for concatenated LDPC-polar codes. As a result, the optimized concatenated OMS decoding yields error-correction performance with CRC-aided successive cancellation list (CA-SCL) decoder of list size 2 on length-1024 polar codes. In addition, the efficient hardware architectures of scalable polar OMS decoder are described and the proposed decoder is reconfigurable to support three code lengths (N = 256, 512, 1024) and two decoding algorithms (2-D OMS and concatenated OMS). The polar OMS decoder implemented on 65 nm CMOS technology achieves a maximum coded throughput of 5.4 Gb/s at Eb/N0= 4 dB for code length 1024 and 7.5 Gb/s at Eb/N0= 3.5 dB for code length 256, which are comparable to the state-of-the-art polar BP decoders. Moreover, a 5.1 Gb/s throughput at Eb/N0= 4 dB is achieved under concatenated OMS decoding mode for code length 1024 with a latency of 200 ns, which is superior to existing CA-SCL decoders that have similar error-correction performance.
The state-of-the-art soft-output decoder for polar codes is a message-passing algorithm based on belief propagation, which performs well at the cost of high processing and storage requirements. In this paper, we propose a low-complexity alternative for soft-output decoding of polar codes that offers better performance but with significantly reduced processing and storage requirements. In particular we show that the complexity of the proposed decoder is only 4% of the total complexity of the belief propagation decoder for a rate one-half polar code of dimension 4096 in the dicode channel, while achieving comparable error-rate performance. Furthermore, we show that the proposed decoder requires about 39% of the memory required by the belief propagation decoder for a block length of 32768.
This paper presents a novel belief propagation (BP) based decoding algorithm for polar codes. The proposed algorithm facilitates belief propagation by utilizing the specific constituent codes that exist in the factor graph, which results in an express journey (XJ) for belief information to propagate in each decoding iteration. In addition, this XJ-BP decoder employs a novel round-trip message passing scheduling method for the increased efficiency. The proposed method simplifies min-sum (MS) BP decoder by 40.6%. Along with the round-trip scheduling, the XJ-BP algorithm reduces the computational complexity of MS BP decoding by 90.4%; this enables an energy-efficient hardware implementation of BP decoding in practice.
This paper presents a novel belief propagation (BP) based decoding algorithm for polar codes. The proposed algorithm facilitates belief propagation by utilizing the specific constituent codes that exist in the factor graph, which results in an express journey (XJ) for belief information to propagate in each decoding iteration. In addition, this XJ-BP decoder employs a novel round-trip message passing scheduling method for the increased efficiency. The proposed method simplifies min-sum (MS) BP decoder by 40.6%. Along with the round-trip scheduling, the XJ-BP algorithm reduces the computational complexity of MS BP decoding by 90.4%; this enables an energy-efficient hardware implementation of BP decoding in practice.
This paper presents a novel propagation (BP) based decoding algorithm for polar codes. The proposed algorithm facilitates belief propagation by utilizing the specific constituent codes that exist in the factor graph, which results in an express journey (XJ) for belief information to propagate in each decoding iteration. In addition, this XJ-BP decoder employs a novel round-trip message passing scheduling method for the increased efficiency. The proposed method simplifies min-sum (MS) BP decoder by 40.6%. Along with the round-trip scheduling, the XJ-BP algorithm reduces the computational complexity of MS BP decoding by 90.4%; this enables an energy-efficient hardware implementation of BP decoding in practice.