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 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.
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.
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.
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 traditional fast successive-cancellation (SC) decoding algorithm can effectively reduce the decoding steps, but the decoding adopts a sub-optimal algorithm, so it cannot improve the bit error performance. In order to improve the bit error performance while maintaining low decoding steps, we introduce a neural network subcode that can achieve optimal decoding performance and combine it with the traditional fast SC decoding algorithm. While exploring how to combine neural network node (NNN) with R1, R0, single-parity checks (SPC), and Rep, we find that the decoding failed sometimes when the NNN was not the last subcode. To solve the problem, we propose two neural network-assisted decoding schemes: a key-bit-based subcode NN-assisted decoding (KSNNAD) scheme and a last subcode NN-assisted decoding (LSNNAD) scheme. The LSNNAD scheme recognizes the last subcode as an NNN, and the NNN with nearly optimal decoding performance gives rise to some performance improvements. To further improve performance, the KSNNAD scheme recognizes the subcode with a key bit as an NNN and changes the training data and label accordingly. Computer simulation results confirm that the two schemes can effectively reduce the decoding steps, and their bit error rates (BERs) are lower than those of the successive-cancellation decoder (SCD).
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.
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.