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IET Communications

Decoding schedule generating method for successive‐cancellation decoder of polar codes

Dan Le, Xianyan Wu, Xiamu Niu

Published Feb 23, 2016• 6 citations
Publisher

Abstract

Successive cancellation (SC) is the first and widely known decoder of polar codes, which has received a lot of attentions. However, its decoding schedule generating methods are still primitive. Based on a newly found factor, this study proposes an online method to generate the decoding schedule of SC decoder by a non‐recursive way. The decoding schedule of SC decoder includes two parts. One is to determine which of likelihood ratios (LRs) can be shared and which of LRs need to be calculated. The other is to select a calculation formula for a LR to be computed. As shown by the comparisons among the proposed method and existing methods, the proposed method solves the first part of the decoding schedule with constant critical path delay and lower space complexity, and solves the second part of the decoding schedule with less calculations. Besides, experimental results show that the proposed method does not affect the error performance of polar codes.

DOI
10.1049/iet-com.2015.0881

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Successive cancellation (SC) is the first and widely known decoder of polar codes, which has received a lot of attentions. However, its decoding schedule generating methods are still primitive. Based on a newly found factor, this study proposes an online method to generate the decoding schedule of SC decoder by a non‐recursive way. The decoding schedule of SC decoder includes two parts. One is to determine which of likelihood ratios (LRs) can be shared and which of LRs need to be calculated. The other is to select a calculation formula for a LR to be computed. As shown by the comparisons among the proposed method and existing methods, the proposed method solves the first part of the decoding schedule with constant critical path delay and lower space complexity, and solves the second part of the decoding schedule with less calculations. Besides, experimental results show that the proposed method does not affect the error performance of polar codes.
Multi-Parallel SCD Polar Coding BEC Polar codes are decoded using successive cancellation (SC) algorithm where likelihood ratios (LRs) for data bits are calculated in a sequential manner, and decisions are made using the calculated LRs.During the decoding of an information bit, the decision results for the predecessor bits are used, and a wrongly decided predecessor bit has negative effect on the accurate calculation of the LR for the information bit being decoded.In SC algorithm, when LR=1, the information bit is decoded as u _i=0, however, such a decision has 50% of chance of being correct.In this paper, we propose improved polar decoders utilizing a number of SC decoders.We consider the case of LR=1, and propose polar decoder structures for the more accurate calculation of the LRs of the successor bits.
Polar codes is promising because they can provably achieve the channel capacity while having an explicit construction method. Lots of work have been done for the bit-based decoding algorithm for polar codes. In this paper, generalized symbol-based successive cancellation (SC) and SC list decoding algorithms are discussed. A symbol-based recursive channel combination relationship is proposed to calculate the symbol-based channel transition probability. This proposed method needs less additions than the maximum-likelihood decoder used by the existing symbol-based polar decoding algorithm. In addition, a two-stage list pruning network is proposed to simplify the list pruning network for the symbol-based SC list decoding algorithm.
Abstract—Polar codes is promising because they can provably achieve the channel capacity while having an explicit construc-tion method. Lots of work have been done for the bit-based decoding algorithm for polar codes. In this paper, generalized symbol-based successive cancellation (SC) and SC list decoding algorithms are discussed. A symbol-based recursive channel combination relationship is proposed to calculate the symbol-based channel transition probability. This proposed method needs less additions than the maximum-likelihood decoder used by the existing symbol-based polar decoding algorithm. In addition, a two-stage list pruning network is proposed to simplify the list pruning network for the symbol-based SC list decoding algorithm. Index Terms—Error control codes, polar codes, successive cancellation decoding, list decoding I.
A two-part successive syndrome-check decoding of polar codes is proposed with the first part successively refining the received codeword and the second part checking its syndrome. A new formulation of the successive-cancellation (SC) decoding algorithm is presented that allows for successively refining the received codeword by comparing the log-likelihood ratio value of a frozen bit with its predefined value. The syndrome of the refined received codeword is then checked for possible errors. In case there are no errors, the decoding process is terminated. Otherwise, the decoder continues to refine the received code-word. The proposed method is extended to the case of SC list (SCL) decoding by terminating the decoding process when the syndrome of the best candidate in the list indicates no errors. Simulation results show that the proposed method reduces the time-complexity of SC and SCL decoders and their fast variants, especially at high signal-to-noise ratios.
A method for efficiently successive cancellation (SC) decoding of polar codes with high-dimensional linear binary kernels (HDLBK) is presented and analyzed. We devise a lll-expressions method which can obtain simplified recursive formulas of SC decoder in likelihood ratio form for arbitrary linear binary kernels to reduce the complexity of corresponding SC decoder. By considering the bit-channel transition probabilities WG(⋅)(⋅∣0)W_{G}^{(\cdot)}(\cdot|0)WG(⋅)​(⋅∣0) and WG(⋅)(⋅∣1)W_{G}^{(\cdot)}(\cdot|1)WG(⋅)​(⋅∣1) separately, a WWW-expressions method is proposed to further reduce the complexity of HDLBK based SC decoder. For a m×mm\times mm×m binary kernel, the complexity of straightforward SC decoder is O(2mNlog⁡N)O(2^{m}N\log N)O(2mNlogN). With WWW-expressions, we reduce the complexity of straightforward SC decoder to O(m2Nlog⁡N)O(m^{2}N\log N)O(m2NlogN) when m≤16m\leq 16m≤16. Simulation results show that 16×1616\times1616×16 kernel polar codes offer significant advantages in terms of error performances compared with 2×22\times22×2 kernel polar codes under SC and list SC decoders.
The authors propose a low complexity list successive cancellation (LCLSC) decoding algorithm, where the advantages of the successive cancellation (SC) decoding and the list successive cancellation (LSC) decoding are both considered. In the proposed decoding, SC decoding instead of LSC decoding is implemented when all information bits from bad subchannels are received reliably. While the reliability of each information bit is estimated by its likelihood ratio (LR), the bit channel quality is measured via its Bhattacharyya parameter. To achieve this goal, the authors introduce two thresholds: LR threshold and Bhattacharyya parameter threshold. Also, the methods to determine them are both elaborated. The numerical results suggest that the complexity of LCLSC decoding is much lower than LSC decoding and can be close to that of SC decoding, while the error performance is almost equal to that of LSC decoding. Especially, when the code rate is in low region, the advantage of our decoding is more obvious.