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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Reduced Complexity Successive-Cancellation Decoding of Polar Codes Based on Linear Approximation

Yongli Yan, Xuanxuan Zhang, Bin Wu

Published Jul 31, 2020• 1 citation
Publisher

Abstract

In this letter, the principle of LLR-based successive-cancellation (SC) polar decoding algorithm is explored. In order to simplify the logarithm and exponential operations in the updating rules for polar codes, we further utilize a piece-wise linear algorithm to approximate the transcendental functions, where the piece-wise linear algorithm only consists of multiplication and addition operations. It is demonstrated that with one properly allowable maximum error δ chosen for success-failure algorithm, performances approach to that of the standard SC algorithm can be achieved. Besides, the complexity reduction is realized by calculating a linear function instead of nonlinear function. Simulation results show that our proposed piece-wise SC decoder greatly reduces the complexity of the SC-based decoders with no loss in error correcting performance.

DOI
10.1587/transfun.2019eal2098

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In this letter, the principle of LLR-based successive-cancellation (SC) polar decoding algorithm is explored. In order to simplify the logarithm and exponential operations in the updating rules for polar codes, we further utilize a piece-wise linear algorithm to approximate the transcendental functions, where the piece-wise linear algorithm only consists of multiplication and addition operations. It is demonstrated that with one properly allowable maximum error δ chosen for success-failure algorithm, performances approach to that of the standard SC algorithm can be achieved. Besides, the complexity reduction is realized by calculating a linear function instead of nonlinear function. Simulation results show that our proposed piece-wise SC decoder greatly reduces the complexity of the SC-based decoders with no loss in error correcting performance.
Although the adaptive successive cancellation list (AD-SCL) algorithm and the segmented-CRC adaptive successive cancellation list (SCAD-SCL) algorithm based on the cyclic redundancy check (CRC) can greatly reduce the computational complexity of the successive cancellation list (SCL) algorithm, these two algorithms discard the previous decoding result and re-decode by increasing L, where L is the size of list. When CRC fails, these two algorithms waste useful information from the previous decoding. In this paper, a simplified adaptive successive cancellation list (SAD-SCL) is proposed. Before the re-decoding of updating value L each time, SAD-SCL uses the existing log likelihood ratio (LLR) information to locate the range of burst error bits, and then re-decoding starts at the incorrect bit with the smallest index in this range. Moreover, when the segmented information sequence cannot get the correct result of decoding, the SAD-SCL algorithm uses SC decoding to complete the decoding of the subsequent segmentation information sequence. Furthermore, its decoding performance is almost the same as that of the subsequent segmentation information sequence using the AD-SCL algorithm. The simulation results show that the SAD-SCL algorithm has lower computational complexity than AD-SCL and SCAD-SCL with negligible loss of performance.
In this paper, we propose a low complexity hybrid ordered statistics decoding (OSD) successive cancellation (SC) decoding algorithm for the polar codes. By replacing smaller size SC decoder with OSD decoder, we can improve the error correcting performance of the SC algorithm. The size of the OSD decoder can be changed to control the trade-off between the decoding complexity and the error correcting performance of the proposed algorithm. We also provide a method to further simplify the proposed algorithm. Simulation results show that the proposed algorithm offers about 0.3 dB gain comparing to the SC at target bit error rate (BER) 10-5with code length N = 1024, 512,256 and code rate R = 1 /3. The impact of the OSD size is also simulated and analyzed.
Recently convolutional polar (cpolar) codes have been proposed. A tensor-network-based successive cancellation (SC) decoding was proposed for them under which cpolar codes were shown to outperform polar codes. In this paper we present the notion of m-bit-channels for cpolar codes and give the recursive construction of m-bit-channels for m=3. Then a log likelihood ratio(LLR)-based SC decoding of complexity order O(Nlog(N)) for cpolar codes is presented. We also present the numerical results for performance evaluation of cpolar codes under SC list (SCL) decoding. Our simulation results show that cpolar codes can achieve the performance of polar codes with a list size reduced by a factor of 4.
For polar codes, perturbing received information can enhance the error-correction performance of successive cancellation (SC) decoding. This is an effective approach for realizing low-latency yet high decoding performance for long polar codes, since each perturbation-enhanced SC (PSC) decoding can be performed in parallel. This paper provides theoretical insights into the soft information perturbation. It first reveals that the PSC decoding can be equivalently viewed as perturbing the SC decoding a posteriori log-likelihood ratio (LLR) of the information bits. Such a revelation enables us to reduce the perturbation complexity by only targeting the information bits, resulting in an improved PSC (IPSC) decoding. By better utilizing the a posteriori LLRs, a set of possibly erroneous estimations can be formed to be perturbed, further reducing the perturbation complexity. Our simulation results show that, for various codeword lengths, the proposed IPSC decoding can achieve a similar performance as the PSC decoding, while yielding significant perturbation complexity reduction.
The Successive-Cancellation List (SCL) algorithm is a popular decoding algorithm for polar codes. Although SCL algorithm overcomes the error propagation problem in polar codes decoding, the improvement of error correction performance needs to pay the price of high latency. To solve this problem, a simplified SCL (SSCL) algorithm is proposed. For some special nodes, the SSCL algorithm can calculate path metric (PM) without traversing the decoding tree to achieve direct decoding, reducing the latency and complexity of decoding. In this paper, a new special node has been discovered, it is also possible to calculate PM without traversing decoding tree. Based on this, we propose an improved SSCL algorithm. Simulation results show that improved SSCL algorithm can further reduce the decoding latency and the loss of error-correction performance is negligible.