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IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

Neural Successive Cancellation List Decoding of Polar Codes

Stefano Negrini, Velio Tralli

Published Aug 1, 2020• 0 citations
Publisher

Abstract

Neural Network Decoders (NNDs) have been recently considered and investigated as an alternative to the classical algorithms for decoding Polar Codes. In particular, a class of partitioned decoders has been proposed where modified Successive Cancellation (SC) or Belief Propagation (BP) algorithms exploit the neural network decoding of short sublocks. Although NNDs work as one-shot decoders with small decoding latency, the performance of these decoders, in comparison with classic approaches, still suffers from some losses; this fact limits their application to codes with short/medium length. In this article we introduce the novel Neural Successive Cancellation List (NSCL) decoder, as a partitioned version of the SC decoder operating on a list of L multiple decoding candidates that are built with the decoded sub-blocks obtained from a set of NNDs working in parallel at each partition. This decoder significantly improves the BER performance of the non-list version under the same code length. Hence, it reduces the intrinsic loss of performance given by the use of NNDs and allows the application of NN-based decoding to longer codewords.

DOI
10.1109/pimrc48278.2020.9217329

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Neural Network Decoders (NNDs) have been recently considered and investigated as an alternative to the classical algorithms for decoding Polar Codes. In particular, a class of partitioned decoders has been proposed where modified Successive Cancellation (SC) or Belief Propagation (BP) algorithms exploit the neural network decoding of short sublocks. Although NNDs work as one-shot decoders with small decoding latency, the performance of these decoders, in comparison with classic approaches, still suffers from some losses; this fact limits their application to codes with short/medium length. In this article we introduce the novel Neural Successive Cancellation List (NSCL) decoder, as a partitioned version of the SC decoder operating on a list of L multiple decoding candidates that are built with the decoded sub-blocks obtained from a set of NNDs working in parallel at each partition. This decoder significantly improves the BER performance of the non-list version under the same code length. Hence, it reduces the intrinsic loss of performance given by the use of NNDs and allows the application of NN-based decoding to longer codewords.
The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a highlevel of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-the art polar decoders such as successive cancellation list and belief propagation decoding.
Polar codes are considered as a competitive candidate for 5G ultra-reliable and low-latency communication (URLLC) channel codes, but its strict latency and reliability requirements pose signicant challenges to the existing decoding schemes, especially in terms of decoding latency. In this paper, we propose a neural network based successive cancellation (NN-SC) decoding algorithm. In the proposed algorithm, neural networks are used to replace the local decoders for rate-R constituent codes because of their one-shot decoding capacity, which greatly reduce the decoding latency and algorithmic complexity. The simulation results indicate that the NN-SC decoding algorithm can achieve comparable reliability performance against the successive cancellation (SC) decoding for a polar code of length 128 and rate 1/6, while reducing the decoding latency by 65.2% when compared with the simplified SC decoding. In addition, for two conventional decoding algorithms: SC and belief propagation (BP) decoding, the proposed algorithm can further reduce the decoding latency by 22.8% and 13.8%, respectively.
Polar code is selected for the 5-th generation of wireless communication standard. Meanwhile, with the demand of low latency in 5G and great success in deep learning area, neural network decoder (NND) becomes a promising candidate for future decoder. However, NND is currently only feasible for very short code lengths. In this paper, we proposed a belief propagation-neural network (BP-NN) algorithm for polar codes based on partitioning. The core of our algorithm is replacing subblock of belief propagation (BP) decoder with NNDs, and using BP decoding framework to connect them. In addition, we also introduce a weight function to complete the message propagation process. Simulation results show the proposed algorithm reduces the decoding delay compared to the traditional BP algorithm and have a well bit error rate (BER) performance. At the same time, it also suitable for long polar codes.
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.
We propose a belief propagation list (BPL) decoder with comparable performance to the successive cancellation list (SCL) decoder of polar codes, which already achieves the maximum likelihood (ML) bound of polar codes for sufficiently large list size L. The proposed decoder is composed of multiple parallel independent belief propagation (BP) decoders based on differently permuted polar code factor graphs. A list of possible transmitted codewords is generated and the one closest to the received vector, in terms of Euclidean distance, is picked. To the best of our knowledge, the proposed BPL decoder provides the best performance of plain polar codes under iterative decoding known so far. The proposed algorithm does not require any changes in the polar code structure itself, rendering the BPL into an alternative to the SCL decoder, equipped with a soft output capability enabling, e.g., iterative detection and decoding to further improve performance. Further benefits are the lower decoding latency than the SCL decoder and the possibility of high throughput implementations. Additionally, we show that a different selection strategy of frozen bit positions can further enhance the error-rate performance of the proposed decoder.
Theoretically, conventional decoders for polar codes can be entirely replaced by neural network (NN) with enough size and enough training, which called NN decoder. But the exponentially increasing training complexity becomes unacceptable when information length increases, which means only decoders for short codes can be trained practically. However, a successive cancellation (SC) decoder for long polar codes can be divided into several SC decoders for short codes, which can be replaced by several short codes NN decoders, then the whole decoder becomes our NN aided SC (NNSC) decoder. Besides, we defined Universal Set of NN, which can be combined into NNSC decoders for any long polar codes. In this paper, the main purpose of constructing NNSC decoder is increasing decoding efficiency of polar codes by taking advantage of NN, and in the meantime ensuring an acceptable performance compared to conventional decoding algorithms.