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IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC)

Simplified Early Stopping Criterion for Polar Codes

Jianming Cui, Jun Li, Yanfei Dong, Xiaojun Zhang, Qingtian Zeng

Published Sep 1, 2018• 4 citations
Publisher

Abstract

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.

DOI
10.1109/icspcc.2018.8567778

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•Feb 3, 2021•0 citations
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.
Belief propagation is one of low latency decoding algorithms for polar codes but it requires relatively high decoding complexity due to its inherent iterative decoding nature. To remedy the problem, early stopping belief propagation algorithm was proposed. Unfortunately, it requires additional complexity to test stopping criterion at each end of decoder iterations. In this paper, we propose a low complexity early stopping belief propagation decoder for polar codes which requires lower complexities not only for stopping criterion test but also for decoding by reducing the number of message updates within the decoder without any performance loss.
The error correction performance of Belief Propagation (BP) decoding for polar codes is satisfactory compared with the Successive Cancellation (SC) decoding. Nevertheless, it has to complete a fixed number of iterations, which results in high computational complexity. This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding. This paper proposes a hybrid technique that combines the “parity-check” with the “G-matrix” to reduce the computational complexity of BP decoder for polar codes. The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process, which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding. We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance. Moreover, mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated. The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding. Simulation results show that the proposed hybrid technique reduces the iterations by about 90% of BP decoding in a high Signal-to-Noise Ratio (SNR) (i.e., 3.5 ∼ 4 ​dB), and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.
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.
In this paper, a novel stopping criterion for Belief Propagation (BP) decoding of polar codes is proposed. The proposed stopping criterion is based on the Bit Difference Ratio (BDR). The BDR stopping method is implemented by monitoring the fluctuation of BDR along with the number of iterations, to decide if the BP decoding process can be terminated. Simulation results indicate that the proposed criterion can provide superiority in iteration reduction compared with the current stopping criteria. Hence, the proposed BDR stopping criterion can effectively reduce the energy waste and decoding latency in systems. Moreover, by loosing the constraint, the proposed stopping criterion can achieve more iteration reduction at the cost of Bit Error Rate (BER) degradation.
In order to reduce the decoding latency, a new early stopping criterion is proposed for belief propagation (BP) decoding. A kind of special processing elements (PEs) of BP decoder called frozen and information PE (FIPE) is selected to predict whether decoding is successful or not. Statistics indicate that FIPE can be considered reliable when the frozen bit is decoded successfully. The proposed criterion is based on the fact that the number of reliable FIPE increase along with iterations and the variation trend is approximate to the ratio of correct information bits. In the term of hardware complexity, the proposed method has a linear correlation with the number of FIPE. This criterion consumes only ‘xor’ and ‘or’ gates to check stopping condition. Simulation results show that the proposed criterion achieves lower latency than Worst Information Bits (WIB) and Frozen Bit Error Rate (FBER) without BLER degradation compared with fixed and G-matrix. Compared with WIB, FBER, Best Frozen Bits (BFB) criterion, the proposed criterion has the lowest hardware complexity.
The belief propagation algorithm is desirable for a polar code based decoder, because of the potentially low latency and the ability of integration in digital signal processing units or other multi-core processor systems to parallelize the computations. Although belief propagation polar code decoder algorithms have the ability for a highly parallelized imple-mentation, the algorithms require many iterations to achieve a comparable frame error rate and bit error rate with respect to a successive cancellation polar code algorithm. The iterative nature of the belief propagation algorithms also result in a higher computational complexity, i.e. O(IN(2log_{2} N-1)) compared to the computational complexity O(Nlog_{2}N) of the successive cancellation decoder algorithm. In this paper we propose several simplifications for a simplified belief propagation algorithm for polar code decoders, where the arithmetic complexity of the nodes is reduced. The proposed belief propagation algorithm shows preliminary results of a net reduction of the arithmetic complexity of ≈ 13%. This reduction is a result of the reduced number of arithmetic operations, i.e., additions, compares, and multiplications, without a lost in error-correcting performance.