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IEEE Communications Letters

A Simplified Decoding Method of Polar Codes Based on Hypothesis Testing

He Sun, Rongke Liu, Chenyu Gao

Published Jan 1, 2020• 24 citations
Publisher

Abstract

In this letter, a simplified successive cancellation decoding algorithm of polar codes is proposed, where a hard decision rule is adopted by exploiting the prior information in frozen bits for better decoding performance. Considering the difference of the node reliability, a hypothesis-testing-based strategy is designed to select reliable unstructured nodes for hard decision. Then the reliable nodes are decoded by the proposed hard decision method without serial recursion, which reduces the decoding latency. Simulation results show the advantages of the proposed method in terms of the decoding latency and error-correction ability compared with the existing methods.

DOI
10.1109/lcomm.2019.2963645

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In this letter, a simplified successive cancellation decoding algorithm of polar codes is proposed, where a hard decision rule is adopted by exploiting the prior information in frozen bits for better decoding performance. Considering the difference of the node reliability, a hypothesis-testing-based strategy is designed to select reliable unstructured nodes for hard decision. Then the reliable nodes are decoded by the proposed hard decision method without serial recursion, which reduces the decoding latency. Simulation results show the advantages of the proposed method in terms of the decoding latency and error-correction ability compared with the existing methods.
In order to reduce the latency of polar codes, several decoding methods have been proposed. However, most of them need a particular structure of nodes in the decoding tree. Thus, they ignore some unstructured nodes. To this end, we propose a modified version of the simplified successive cancellation decoder based on node error probability to complement the structured scheme. By a proper design, simulation results in additive white Gaussian noise channel show that the proposed method can efficiently reduce the decoding latency of the structured scheme while keeping the error performance almost unchanged.
In this letter an improved method for the successive-cancellation decoding of polar codes is proposed. To avoid computations associated with redundant tree-traversals and syndrome calculations, recursive properties of polar codes are newly exploited in the proposed algorithm. Instead of computing a syndrome vector at every node, some syndrome vectors are directly obtained by recursively decomposing the syndrome vector computed previously. Furthermore, a modified syndrome check rule is proposed to prune unnecessary sub-trees efficiently. Compared with the latest pruning method, the proposed method reduces the latency by 23% for a (2048, 1024) polar code without sacrificing the error-correcting performance.
Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm improves the situation in theoretically but not performs well as expected in practical for the workload of nodes identification and the existence of many short blocks. Meanwhile, Neural network (NN) based decoders have appeared as potential candidates to replace conventional decoders for polar codes. But the exponentially increasing training complexity with information bits is unacceptable which means it is only suitable for short codes. In this paper, we present an improvement that increases decoding efficiency without degrading the error-correction performance. The long polar codes are divided into several sub-blocks, some of which can be decoded adopting fast maximum likelihood decoding method and the remained parts are replaced by several short codes NN decoders. The result shows that time steps the proposed algorithm need only equal to 79.8% of fast simplified successive-cancellation decoders require. Moreover, it has up to 21.2 times faster than successive-cancellation decoding algorithm. More importantly, the proposed algorithm decreases the hardness when applying in some degree.
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.
In the case of short code, polar code demonstrates superior performance compared with Low Density Parity Check (LDPC) code. Particularly in low coding rate scenario, the complexity of Polar code encoding and decoding is significantly lower than that of LDPC code. The technological advantage of Polar code makes it of great value in special application scenarios such as satellite communication and ocean communication. The polar coding scheme can significantly improve the transmission reliability of the communication system, because the satellite spread spectrum communication system generally adopts short code design.In the research of decoding algorithm, the original Serial Cancellation (SC) decoding algorithm has simple rules, but the decoding effect is not ideal under the limited code length, and the serial decoding mechanism leads to large decoding delay. The Successive Cancellation List (SCL) decoding algorithm improves decoding performance by increasing the number of decoding search path. However, maintaining multiple decoding paths can multiply the decoding complexity. Fast node-based decoding algorithm aims to accelerate decoding and reduce latency by defining and simplifying the decoding process for specific nodes, yet they do not optimize the decoding paths. In view of the above problems, this paper proposes a Simplified Parity Check-based Cyclic Redundancy Check (CRC)-Aided Successive Cancellation List (S-PC-CASCL) decoding algorithm. Simulation results demonstrate that the proposed S-PC-CASCL maintains excellent error correction performance while reducing the average list size by up to 16 % under low Signal Noise Ratio (SNR) conditions, thereby lowering computational complexity and decoding latency compared with other widely used polar decoding methods.
In this paper, we propose a simplified multi-bit successive cancellation list (SMSCL) decoding method for polar codes. In the proposed SMSCL decoding, frozen bits are ignored, and multiple information bits are intermediately decoded at each decision step. In addition, a modified two-stage pruning network is proposed to reduce the complexity of path pruning in SMSCL decoding. Compared to the existing multi-bit SCL decoders, the SMSCL decoder can achieve significant latency and complexity reduction over a wide range of code rates.