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IEEE Transactions on Very Large Scale Integration (VLSI) Systems

Efficient Soft Cancelation Decoder Architectures for Polar Codes

Jun Ting Lin, Zhiyuan Yan, Zhongfeng Wang

Published Jul 12, 2016• 12 citations
Publisher

Abstract

The flooding belief propagation (FO-BP) and the soft-cancelation (SCAN) algorithms are the two most popular soft-output BP algorithms for the decoding of capacity-achieving polar codes. The FO-BP algorithm has high throughput at the cost of performance degradation in high signal-to-noise ratio (SNR) region or with large block length. The SCAN algorithm has much better decoding performance while suffering from long decoding latency and low throughput. In this paper, an improved BP algorithm, named reduced complexity soft-cancelation (RCSC) algorithm, is proposed. Compared with the SCAN algorithm, the number of memory entries required by the RCSC algorithm is reduced by more than 50% in general, while achieving comparable or even better (e.g., when block size N = 215) decoding performance. When block size is large (e.g., N ≥ 215), the proposed RCSC algorithm reduces the required memory entries by more than 23% compared with the state-of-the-art FO-BP algorithm. The numerical results show that the error performance improvement of the RCSC algorithm is more significant when the SNR increases. For a different tradeoff, a reduced latency soft-cancelation (RLSC) algorithm is proposed to reduce the decoding latency and increase the throughput of the RCSC algorithm while slightly sacrificing decoding performance. Finally, the optimized VLSI architectures are presented for the RCSC and RLSC algorithms, respectively. The synthesis results demonstrate the efficiency of the proposed algorithms and architectures.

DOI
10.1109/tvlsi.2016.2577883

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The flooding belief propagation (FO-BP) and the soft-cancelation (SCAN) algorithms are the two most popular soft-output BP algorithms for the decoding of capacity-achieving polar codes. The FO-BP algorithm has high throughput at the cost of performance degradation in high signal-to-noise ratio (SNR) region or with large block length. The SCAN algorithm has much better decoding performance while suffering from long decoding latency and low throughput. In this paper, an improved BP algorithm, named reduced complexity soft-cancelation (RCSC) algorithm, is proposed. Compared with the SCAN algorithm, the number of memory entries required by the RCSC algorithm is reduced by more than 50% in general, while achieving comparable or even better (e.g., when block size N = 215) decoding performance. When block size is large (e.g., N ≥ 215), the proposed RCSC algorithm reduces the required memory entries by more than 23% compared with the state-of-the-art FO-BP algorithm. The numerical results show that the error performance improvement of the RCSC algorithm is more significant when the SNR increases. For a different tradeoff, a reduced latency soft-cancelation (RLSC) algorithm is proposed to reduce the decoding latency and increase the throughput of the RCSC algorithm while slightly sacrificing decoding performance. Finally, the optimized VLSI architectures are presented for the RCSC and RLSC algorithms, respectively. The synthesis results demonstrate the efficiency of the proposed algorithms and architectures.
The belief propagation (BP) decoding algorithm not only is an alternative to the successive cancelation (SC) decoders of polar codes, but also provides soft outputs that are necessary for joint detection and decoding. The BP decoders with the flooding schedule achieve high throughput with excessive hardware cost especially when the block length is large. The soft-cancelation (SCAN) decoders for polar codes have reduced memory complexity compared to the BP decoders based on the flooding schedule. The simplified SC aided reduced complexity soft-cancelation (S-RCSC) decoders further reduce the computational and memory complexity of the SCAN decoders at the cost of negligible error performance degradation. Both the SCAN and S-RCSC decoders have limited throughput due to their serial decoding schedules. In this paper, we first propose an improved S-RCSC (IS-RCSC) decoding algorithm and then present a high throughput decoder architecture based on our IS-RCSC algorithm. Our IS-RCSC decoding algorithm performs the message passing on a binary tree representation of a polar code. Compared to the S-RCSC decoding algorithm, our IS-RCSC decoding algorithm accelerates the computing of the returned soft messages when certain types of nodes are activated. The corresponding hardware architecture of our IS-RCSC decoder is also proposed. In terms of area efficiency, the hardware implementation results demonstrate that our IS-RCSC decoders are 19% to 43% better than decoders in the literature.
Polar Codes can provably achieve the capacity of discrete memoryless channels. In order to make practical, it is necessary to propose efficient hardware decoder architectures. In this paper, the first hardware decoder architecture implementing the Soft-output CANcellation (SCAN) decoding algorithm, is presented. This decoder was implemented on Field Programmable Gate Array (FPGA) devices. The proposed architecture is parametrizable for any number of iterations without adding hardware complexity. The SCAN decoder architecture is compared to another soft-output decoder that implements a Belief Propagation (BP) algorithm. The SCAN decoder can reach a higher throughput than a BP decoder, with a lower memory footprint. Moreover, only one iteration with the SCAN algorithm leads to better decoding performance than 50 iterations of the BP algorithm.
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.
Belief propagation (BP) algorithm of polar codes suffers from very high computational complexity when the iteration number becomes larger. In this paper, an early stopping criterion is proposed to avoid unnecessary iterations efficiently. The proposed only needs to detect whether the proportion of unchanged soft-output messages in a detection space exceeds a threshold. The proposed iteration can achieve a desired trade-off between complexity and decoding performance. Simulation results have shown that when the maximum iteration number is 40, the flooding BP (FO-BP) decoder with the proposed criterion can reduce 82.17% of iterations at 3.5dB compared with the FO-BP decoder without early stopping criterion. The proposed criterion costs Nl32 additions and Nl32 comparisons, where N indicates the code length, which effectively reduces the computational complexity.
This paper proposes a novel iterative decoder based on concatenated belief propagation (BP) for CRC-aided polar codes. Compared to the conventional BP-based decoders for polar codes, soft cancellation (SCAN) decoder can generate a log likelihood ratio (LLR) of coded bit with lower computational complexity without sacrificing the detection capability. Unfortunately, its performance is not as good as that of CRC-aided successive cancellation list decoder (SCLD) although SCAN decoder has advantage of hardware implementation. To compensate the performance gap, we exploit CRC structure for not only error detection but also error correction with the assistance of its error correction capability at a short code length by exchanging LLRs between SCAN decoder and BP decoder on the basis of CRC. Moreover, the sub-optimal criterion for selecting a parity check matrix of CRC for BP decoder is proposed. Finally, computer simulations are conducted to confirm the validity of our proposed method. The proposed method can obtain the gain of about 0.6 dB at BER=10-3compared to the native SCAN decoder without requiring huge memory size as in SCLD.
The soft cancellation decoding of polar codes achieves a better performance than the belief propagation decoding with lower computational time and space complexities. However, because the soft cancellation decoding is based on the successive cancellation decoding, the decoding efficiency and performance with finite-length blocks can be further improved. Exploiting the idea of the successive cancellation list decoding, the soft cancellation decoding can be improved in two aspects: one is by adding branch decoding to the error-prone information bits to increase the accuracy of the soft information, and the other is through using partial iterative decoding to reduce the time and computational complexities. Compared with the original method, the improved soft cancellation decoding makes progress in the error correction performance, increasing the decoding efficiency and reducing the computational complexity, at the cost of a small increase of space complexity.