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arXiv:1901.05459 · International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY)

Permutation Decoding of Polar Codes

Mikhail Kamenev, Yulia Kameneva, Oleg Kurmaev, Alexey Maevskiy

Published Oct 1, 2019• 32 citations
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Abstract

A new permutation decoding approach for polar codes is presented. The proposed decoder can be used to achieve the error correction performance of a successive cancellation list (SCL) decoder, while it can either improve latency of the SCL decoder or decrease its hardware complexity. As opposed to the SCL algorithm, the proposed permutation algorithm can be implemented without sorting operation. It is shown that the error correction performance of the algorithm is similar to that of the SCL decoder for polar codes. Moreover, a new construction aiming to improve the error correction performance of polar codes under the proposed algorithm is presented.

DOI
10.1109/redundancy48165.2019.9003333

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A new permutation decoding approach for polar codes is presented. The proposed decoder can be used to achieve the error correction performance of a successive cancellation list (SCL) decoder, while it can either improve latency of the SCL decoder or decrease its hardware complexity. As opposed to the SCL algorithm, the proposed permutation algorithm can be implemented without sorting operation. It is shown that the error correction performance of the algorithm is similar to that of the SCL decoder for polar codes. Moreover, a new construction aiming to improve the error correction performance of polar codes under the proposed algorithm is presented.
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.
The Successive-Cancellation List (SCL) decoding algorithm is one of the most promising approaches towards practical polar code decoding. It is able to provide a good trade-off between error-correction performance and complexity, tunable through the size of the list. In this paper, we show that in the conventional formulation of SCL, there are redundant calculations which do not need to be performed in the course of the algorithm. We simplify SCL by removing these redundant calculations and prove that the proposed simplified SCL and the conventional SCL algorithms are equivalent. The simplified SCL algorithm is valid for any code and can reduce the time-complexity of SCL without affecting the space complexity.
By adopting successive cancellation list decoding (SCL), polar codes demonstrate competitive error correction performance over LDPC and Turbo codes. However, SCL decoding suffers from high computational complexity and long decoding latency, especially when the list size is very large. Successive cancellation flip (SCF), as another decoding algorithm that can achieve high error correction performance, has a complexity that is close to that of successive cancellation (SC) decoding. With the observation that SCL and SCF decoding are similar at giving more chances to inspect possible codewords simultaneously or sequentially, a novel hybrid decoder is proposed in this paper, which essentially combines the ideas of SCF and SCL decoders. Moreover, in order to compensate for the degradation of performance caused by the reduction of path splitting and further reduce the decoding latency, the convolutional polar codes are adopted with a designed bit-flipping set. Simulation results demonstrate that the proposed decoder achieves the reduction of decoding latency while attaining better performance than conventional CRC-aided SCL decoder.
Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths. However, the application of SCL decoding in low-latency communication scenarios is limited due to its sequential nature. To reduce the decoding latency, developing tailored fast and efficient list decoding algorithms of specific polar constituent codes (special nodes) is a promising solution. Recently, fast list decoding algorithms are proposed by considering special nodes with low code rates. Aiming to further speedup the SCL decoding, this paper presents fast list decoding algorithms for two types of high-rate special nodes, namely single-parity-check (SPC) nodes and sequence rate one or single-parity-check (SR1/SPC) nodes. In particular, we develop two classes of fast list decoding algorithms for these nodes, where the first class uses a sequential decoding procedure to yield decoding latency that is linear with the list size, and the second further parallelizes the decoding process by pre-determining the redundant candidate paths offline. Simulation results show that the proposed list decoding algorithms are able to achieve up to 70.7% lower decoding latency than state-of-the-art fast SCL decoders, while exhibiting the same error-correction performance.
Successive-cancellation list (SCL) decoding is an algorithm that provides very good error-correction performance for polar codes. However, its hardware implementation requires a large amount of memory, mainly to store intermediate results. In this paper, a partitioned SCL algorithm is proposed to reduce the large memory requirements of the conventional SCL algorithm. The decoder tree is broken into partitions that are decoded separately. We show that with careful selection of list sizes and number of partitions, the proposed algorithm can outperform conventional SCL while requiring less memory.
The successive-cancellation list (SCL) and successive-cancellation flip (SCF) decoding can be used to improve the performance of polar codes, especially for short to moderate length codes. However, their serial decoding nature results in significant decoding latencies. Implementing some operations in parallel can reduce their decoding latencies. This paper presents fast implementations of the SCL and SCF decoders. In particular, we propose fast parallel list decoders for five newly identified types of nodes in the decoding tree of a polar code, which significantly improves the decoding latency. We also present novel fast SCF decoders that decode some special nodes in the decoding tree of a polar code without serially computing bit log-likelihood ratios. Using our proposed fast parallel SCF decoders, we observed an improvement up to 81% with respect to the original SCF decoder. This significant reduction in the decoding latency is observed without sacrificing the bit-error-rate performance of the code.