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 successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding quantum polar codes and show that it inherits the high performance and low complexity of the classical case, and can approximate the quantum MLD for certain channels. We apply SCL decoding to a novel version of quantum polar codes based on the polarization weight (PW) method, which entirely avoids the need for small amounts of entanglement assistance apparent in previous quantum polar code constructions. When used to find the precise error pattern, the quantum SCL decoder (SCL-E) shows competitive performance with surface codes of similar size and low-density parity check codes of similar size and rate. The SCL decoder may instead be used to approximate the probability of each equivalence class of errors, and then choose the most likely class. We benchmark this class-oriented decoder (SCL-C) against the SCL-E decoder and find a noticeable improvement in the logical error rate. This improvement stems from the fact that the contributions from just the low-weight errors give a reasonable approximation to the error class probabilities. Both SCL-E and SCL-C maintain the complexity O(LN log N) of SCL for code sizeNand list size L.
Due to the low-latency and high-reliability requirements of 5G, low-complexity node-based successive cancellation list (SCL) decoding has received considerable attention for use in 5G communications systems. By identifying special constituent codes in the decoding tree and immediately decoding these, node-based SCL decoding provides a significant reduction in decoding latency compared to conventional SCL decoding. However, while there exists many types of nodes, the current node-based SCL decoders are limited by the lack of a more generalized node that can efficiently decode a larger number of different constituent codes to further reduce the decoding time. In this paper, we extend a recent generalized node, the sequence repetition (SR) node, to SCL decoding, and describe the first implementation of an SR-List decoder. By merging certain SR-List decoding operations and applying various optimizations for 5G New Radio (NR) polar codes, our optimized SR-List decoding algorithm increases the throughput by almost2×compared to a similar state-of-the-art node-based SCL decoder. We also present our hardware implementation of the optimized SR-List decoding algorithm which supports all 5G NR polar codes. Synthesis results show that our SR-List decoder can achieve a2.94Gbpsthroughput and6.70Gbpsm−1m2area efficiency forL=8.