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IEEE Wireless Communications and Networking Conference

Simplified Successive-Cancellation List Decoding of Non-Binary Polar Codes with Rate-1 Node

Baoping Feng, Rongke Liu, He Sun

Published May 1, 2020• 6 citations
Publisher

Abstract

In this paper, one of the constituent codes, Rate-1 node, is used to simplify Successive-Cancellation List (SCL) decoding of non-binary polar codes for reducing the decoding complexity. First, we derive the Logarithmic Likelihood Ratio based (LLR-based) path metric of non-binary polar codes in SCL decoding. Then we propose that the path metric only depends on the LLR value at the top of Rate-1 node tree, which avoids traversing a complete decoding tree in non-binary SCL decoding. Finally, we design a novel reliability metric, which is used to select the unreliable symbols from the LLRs at the top of Rate-1 node tree. By the proposed metric, we select the unreliable symbols to generate the candidate paths, which avoids splitting paths for all symbols of Rate-1 node in the conventional SCL decoding. Simulation results show that the proposed non-binary SCL decoding reduces significantly the computation and time complexity without the performance loss.

DOI
10.1109/wcnc45663.2020.9120673

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IEEE Access•Jan 1, 2019•9 citations
In this paper, one of the constituent codes, Rate-1 node, is used to simplify Successive-Cancellation List (SCL) decoding of non-binary polar codes for reducing the decoding complexity. First, we derive the Logarithmic Likelihood Ratio based (LLR-based) path metric of non-binary polar codes in SCL decoding. Then we propose that the path metric only depends on the LLR value at the top of Rate-1 node tree, which avoids traversing a complete decoding tree in non-binary SCL decoding. Finally, we design a novel reliability metric, which is used to select the unreliable symbols from the LLRs at the top of Rate-1 node tree. By the proposed metric, we select the unreliable symbols to generate the candidate paths, which avoids splitting paths for all symbols of Rate-1 node in the conventional SCL decoding. Simulation results show that the proposed non-binary SCL decoding reduces significantly the computation and time complexity without the performance loss.
Path Metric (PM) is the reference standard for decoding path reliability in successive cancellation list (SCL) algorithm, which needs to be updated in real time with the verdict of bits, and is the main component of decoding complexity of the SCL algorithm in addition to the recurrence of log-likelihood ratio (LLR) information. Most schemes for optimizing the decoding complexity of the SCL algorithm focus on reducing the recurrence of LLR, and relatively little research has been done on reducing the computational complexity of PM. Based on this current situation, this paper proposes an optimization scheme for the SCL algorithm flow by analyzing the execution process and the role of PM in the SCL algorithm. Meanwhile, the optimized simplified SCL based double-repetition nodes (SSCL-D-Rep) algorithm is proposed for the phenomenon of increasing PM computation in the SSCL algorithm and the SSCL-D-Rep algorithm. Simulation results show that the SSCL-D-Rep algorithm proposed in this paper can reduce the system complexity without losing the bit error rate (BER).
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.
Polar codes are capacity achieving error correcting codes that can be decoded through the successive-cancellation algorithm. To improve its error-correction performance, a list-based version called successive-cancellation list (SCL) has been proposed in the past, that however substantially increases the number of time-steps in the decoding process. The simplified SCL (SSCL) decoding algorithm exploits constituent codes within the polar code structure to greatly reduce the required number of time-steps without introducing any error-correction performance loss. In this paper, we propose a faster decoding approach to decode one of these constituent codes, the Rate-1 node. We use this Rate-1 node decoder to develop Fast-SSCL. We demonstrate that only a list-size-bound number of bits needs to be estimated in Rate-1 nodes and Fast-SSCL exactly matches the error-correction performance of SCL and SSCL. This technique can potentially greatly reduce the total number of time-steps needed for polar codes decoding: analysis on a set of case studies show that Fast-SSCL has a number of time-steps requirement that is up to 66.6% lower than SSCL and 88.1% lower than SCL.
Polar codes are capacity achieving error correcting codes that can be decoded through the successive-cancellation algorithm. To improve its error-correction performance, a list-based version called successive-cancellation list (SCL) has been proposed in the past, that however substantially increases the number of time-steps in the decoding process. The simplified SCL (SSCL) decoding algorithm exploits constituent codes within the polar code structure to greatly reduce the required number of time-steps without introducing any error-correction performance loss. In this paper, we propose a faster decoding approach to decode one of these constituent codes, the Rate-1 node. We use this Rate-1 node decoder to develop Fast-SSCL. We demonstrate that only a list-size-bound number of bits needs to be estimated in Rate-1 nodes and Fast-SSCL exactly matches the error-correction performance of SCL and SSCL. This technique can potentially greatly reduce the total number of time-steps needed for polar codes decoding: analysis on a set of case studies show that Fast-SSCL has a number of time- steps requirement that is up to 66.6% lower than SSCL and 88.1% lower than SCL.
Successive cancellation (SC) decoding algorithm and successive cancellation list (SCL) decoding algorithm are two common decoding methods for polar codes. The SC decoding algorithm has low complexity, but in its decoding process, the bits with small channel indices are used to assist the decoding of the bits with large channel indices. Therefore, the bit being decoded depends on the bits that have already been decoded which causes error propagation. On the basis of SC decoding, the SCL decoding algorithm overcomes the problem of error propagation by widening the path search width and retaining multiple paths at the same time in the decoding process. However, the complexity of SCL decoding is higher than that of SC decoding. Without changing the performance of the SCL decoding algorithm, we propose a low-complexity SCL decoding algorithm based on path metric (PM). After the last frozen bit is decoded, the path with the smallest PM is selected, and the subsequent nodes adopt SC decoding. Through this combination of SCL decoding and SC decoding, the complexity of the SCL decoding algorithm can be effectively reduced while the SCL decoding performance remains unchanged, especially in the case of high code rates.
The successive cancellation list (SCL) decoding of polar codes can achieve a performance close to that of maximum-likelihood decoding. Nevertheless, a large list size results in high-computational complexity. In this paper, a successive cancellation priority (SCP) decoding algorithm is proposed to reduce the time complexity. The SCP decoder performs a priority-first decoding, which is composed of a priority queue and a trellis. During the SCP decoding, the priority queue interacts with the trellis iteratively. Conceptually, the priority queue stores the priority information and guides the extension of the candidate path. The trellis calculates and stores the intermediate results. Since most of the unnecessary path extensions are avoided by using the priority queue, the time complexity of the SCP decoder is much lower than that of the standard SCL decoder. Then, a quantized priority queue is introduced to avoid the comparison operations in the path selection and to simplify the SCP decoder. Furthermore, we prove that the path extension of the SCP decoder is equivalent to the extension of the most reliable paths of the standard SCL decoder. Thus, the SCP decoder can achieve the same decoding performance as that of the standard SCL decoder.