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IEEE Communications Letters

An Improvement of Modified Successive-Cancellation Decoder for Polar Codes

Zhiliang Huang, Chunjuan Diao, Jianxin Dai, Chunjiang Duanmu, Xia Wu, Ming Chen

Published Nov 19, 2013• 10 citations
Publisher

Abstract

An improvement is introduced of the modified successive-cancellation (MSC) decoding for polar codes, in which local decoders at rate-other nodes are simplified. This improvement reduces the decoding latency and complexity of the MSC decoding with no sacrifice in error performance. Furthermore, in our method, the decoding latency decreases rapidly with increasing signal-to-noise ratio. Significant latency and complexity reductions are shown by simulation results.

DOI
10.1109/lcomm.2013.110413.132136

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An improvement is introduced of the modified successive-cancellation (MSC) decoding for polar codes, in which local decoders at rate-other nodes are simplified. This improvement reduces the decoding latency and complexity of the MSC decoding with no sacrifice in error performance. Furthermore, in our method, the decoding latency decreases rapidly with increasing signal-to-noise ratio. Significant latency and complexity reductions are shown by simulation results.
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.
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.
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 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.
Polar codes represent an emerging correcting codes with power to approach the capacity of a discrete memoryless channel.However, the decoding performance of polar codes with traditional successive cancellation (SC) algorithm cannot match that of the low-density parity-check or Turbo codes.In this paper, a modified successive cancellation stack (MSCS) polar decoder is proposed.Unlike the original SC stack polar (SCS) decoders, we propose a modified path that can significantly reduce latency of SCS decoders.Simulation results in the binary-input additive white Gaussian noise channel show that modified algorithm has the slightly performance as the SCS algorithm.Moreover, the time and space complexity of the MSCS decoder is much lower than that of the SCS and can be very close to that of the SC in the high SNR regime.