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IEEE Communications Letters

Learning to Construct Nested Polar Codes: An Attention-Based Set-to-Element Model

Yang Li, Zhitang Chen, Guochen Liu, Yik‐Chung Wu, Kai‐Kit Wong

Published Sep 20, 2021• 18 citations
Publisher

Abstract

As capacity-achieving codes under successive cancellation (SC) decoding, nested polar codes have been adopted in 5G enhanced mobile broadband. To optimize the performance of the code construction under practical decoding, e.g. SC list (SCL) decoding, artificial intelligence based methods have been explored in the literature. However, the structure of nested polar codes has not been fully exploited for code construction. To address this issue, this letter transforms the original combinatorial optimization problem for the construction of nested polar codes into a policy optimization problem for sequential decision, and proposes an attention-based set-to-element model, which incorporates the nested structure into the policy design. Based on the proposed architecture for the policy, a gradient based algorithm for code construction and a divide-and-conquer strategy for parallel implementation are further developed. Simulation results demonstrate that the proposed construction outperforms the state-of-the-art nested polar codes for SCL decoding.

DOI
10.1109/lcomm.2021.3114118

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As capacity-achieving codes under successive cancellation (SC) decoding, nested polar codes have been adopted in 5G enhanced mobile broadband. To optimize the performance of the code construction under practical decoding, e.g. SC list (SCL) decoding, artificial intelligence based methods have been explored in the literature. However, the structure of nested polar codes has not been fully exploited for code construction. To address this issue, this letter transforms the original combinatorial optimization problem for the construction of nested polar codes into a policy optimization problem for sequential decision, and proposes an attention-based set-to-element model, which incorporates the nested structure into the policy design. Based on the proposed architecture for the policy, a gradient based algorithm for code construction and a divide-and-conquer strategy for parallel implementation are further developed. Simulation results demonstrate that the proposed construction outperforms the state-of-the-art nested polar codes for SCL decoding.
The Successive Cancellation List (SCL) algorithm is a widely used decoding technique in communication systems. However, constructing the critical set for SCL decoding is a challenging task, as it requires a large number of computations and can lead to significant decoding delays. In this paper, a new approach to critical set construction for SCL decoding is proposed, which is based on deep learning of neural networks with special structure and activation functions.The proposed method is shown to significantly reduce the cardinality of the critical set required for achieving the target frame error rate, when used with an SCL decoder with a list size of 8. Simulation results demonstrate that the proposed method outperforms existing methods in terms of reducing decoding delay, while maintaining high decoding accuracy.The key innovation of the proposed approach lies in the use of deep learning techniques to learn the structure of the critical set, which enables the construction of a more efficient and compact set. This approach has the potential to significantly improve the performance of SCL decoding in practical communication systems, where decoding delay is a critical factor.
Pre-transformed polar codes constitute a broad class of codes constructed through the serial concatenation of outer codes and polar codes, enhancing the performance of standalone polar codes either by improving the weight distribution or by increasing the error-decay rate. Deep polar codes, a novel variant within this class, are constructed through a pre-transformation that involves a series of nested polar codes with increasing dimensions across layers. The proposed successive cancellation list with backpropagation parity check (SCL-BPC) decoder exploits the parity equations naturally arising from this nested encoding structure. In certain scenarios, deep polar codes with SCL-BPC decoding demonstrate superior performance compared to other pre-transformed polar codes. However, the SCL-BPC algorithm incurs additional decoding complexity and results in uneven decoding times. To address these issues, we investigate the matrix representation of the pre-transformation in deep polar codes and develop efficient implementation solutions for SCL-BPC decoding. Additionally, we introduce a low-complexity approach to SCL-BPC, which exhibits only a marginal reduction in performance.
Polar codes have been selected as the channel coding scheme for the Enhanced Mobile Broadband (eMBB) control channel in 5G, which requires short length codes. One of the main challenges in utilizing polar codes is the design of low-complexity decoders with adequate error-correcting performance. The Successive Cancellation (SC) decoder was introduced as the first algorithm enabling polar codes to achieve the channel capacity for long codelengths. However, for shorter codelengths, this decoder does not provide satisfactory error-correction performance. To address this limitation, the Successive Cancellation List (SCL) decoder has been proposed, which performs decoding by maintaining a list of candidate paths and selecting the best one based on a path metric. In this paper, we propose improving the error-correction performance of the SCL decoder using concatenated Cyclic Redundancy Check (CRC) codes and Long Short-Term Memory (LSTM) network. Simulation results demonstrate that the proposed method outperforms the Belief Propagation (BP) decoder in terms of Bit Error Rate (BER) curves. Furthermore, the accuracy of the LSTM model in this study improves from 73 percent in previous research to 93.77 percent.
Polar codes, as the coding scheme for the control channel in fifth-generation mobile communication technology (5G), have attracted widespread attention since their proposal. As a mainstream decoding algorithm for polar codes, the successive cancellation list (SCL) decoder usually improves the error correction performance by increasing the list size, but this method suffers from the problems of high decoding complexity. To address this problem, this paper proposes a layered-search bit-flipping (LS-SCLF) decoding algorithm based on SCL decoding. Firstly, a new flip-bit metric is proposed, which derives a formula to approximate the probability of an error occurring in an information bit. This formula introduces a perturbation parameter to improve the calculation accuracy. Secondly, a compromise scheme for determining the perturbation parameter is proposed. The scheme uses Monte Carlo simulation to determine an optimized parameter for the precise positioning of the first erroneous decoded bit under different decoding conditions. Finally, a layered search strategy is adopted to sequentially search the erroneous decoded bits from the low order to high order, which can correct up to multiple bits at the same time. Simulation results show that the proposed algorithm achieves improved error correction performance with a slight increase in decoding complexity compared to the generalized SCL-Flip (GSCLF) decoding algorithm. This algorithm also achieves a good balance between the error correction performance and decoding complexity.
Polar codes have been chosen by 3GPP as the official error-correcting codes in the control plane of 5G NR enhanced Mobile Broadband (eMBB) due to their low complexity decoding and near-DMC capacity achievement. Recently, deep learning methods have produced promising results in many fields, including linear and polar code decoding. Using end-to-end DL approach provides flexibility, thus empowering us to integrate powerful DL algorithms into channel decoders. In this paper, we propose a novel one-shot decoding framework for polar codes using Attention-based Recurrent Neural Network (ATRNN). Furthermore, we evaluate the decoding performance of ATRNN using bit error rate (BER) and compare it with the state-of-the-art techniques such as successive cancellation (SC).
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×\bm {2\times }2×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 a2.94 Gbps2.94 \,\mathrm{Gbps}2.94Gbpsthroughput and6.70 Gbpsm−1 m2 6.70 \,\mathrm{Gbps}\mathrm{m}^{-1}\,\mathrm{m}^{2}\,6.70Gbpsm−1m2area efficiency forL=8\bm {L=8}L=8.