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IEEE Communications Letters

Enhancing Belief Propagation Decoding of Polar Codes: A Reinforcement Learning Approach

Mohsen Moradi, Salman Habib, David G. M. Mitchell

Published Apr 9, 2025• 3 citations
Publisher

Abstract

Short block-length polar-like codes showcase exceptional error correction performance (ECP) using sequential decoding or successive cancellation list decoding with a large list size. However, achieving a high level of reliability with these methods involves high-latency decoding. To meet the growing demand for low-latency communication with acceptable complexity, belief propagation (BP) decoding emerges as an attractive option, although its ECP is known to fall short of those high-latency alternatives. In this paper, we propose an enhanced BP decoding approach for polar codes, leveraging reinforcement learning (RL) to optimize the message-passing schedule. Moreover, we investigate the design of the polar code rate profile and corresponding Tanner graph representation to enhance the benefits of RL. Numerical results demonstrate a performance gain of more than 1 dB for polar codes with a length of 128 and a rate of 0.5 compared to conventional BP decoding alone at highEb/N0values, demonstrating the promise of the proposed approach.

DOI
10.1109/lcomm.2025.3559466

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•Feb 3, 2022•0 citations
Short block-length polar-like codes showcase exceptional error correction performance (ECP) using sequential decoding or successive cancellation list decoding with a large list size. However, achieving a high level of reliability with these methods involves high-latency decoding. To meet the growing demand for low-latency communication with acceptable complexity, belief propagation (BP) decoding emerges as an attractive option, although its ECP is known to fall short of those high-latency alternatives. In this paper, we propose an enhanced BP decoding approach for polar codes, leveraging reinforcement learning (RL) to optimize the message-passing schedule. Moreover, we investigate the design of the polar code rate profile and corresponding Tanner graph representation to enhance the benefits of RL. Numerical results demonstrate a performance gain of more than 1 dB for polar codes with a length of 128 and a rate of 0.5 compared to conventional BP decoding alone at highEb/N0values, demonstrating the promise of the proposed approach.
Belief propagation (BP) has attracted increasing attention due to its high parallelism. In this letter, a correction method is proposed to improve the block error rate (BLER) performance of the BP decoder for polar codes so that it is comparable to that of the successive cancellation list (SCL) decoder. Compared with BP flipping (BPF) decoding, the proposed decoder focuses on prior knowledge of the code bits in the factor graph. Two strategies have been proposed to construct the correction set. The simulation results show that the BPC decoder exhibits a BLER similar to that of BPF decoder while reducing the average latency and complexity by half. In addition, the BLER of the BPC decoder can approach that of the cyclic redundancy check (CRC)-aided SCL (CA-SCL) decoder in regions with low and medium signal-to-noise ratios (SNRs).
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.
Owing to its high parallelism, belief propagation (BP) decoding is highly amenable to high-throughput implementations and thus represents a promising solution for meeting the ultra-high peak data rate of future communication systems. However, for polar codes, the error-correcting performance of BP decoding is far inferior to that of the widely used CRC-aided successive cancellation list (SCL) decoding algorithm. To close the performance gap to SCL, BP list (BPL) decoding expands the exploration of candidate codewords through multiple permuted factor graphs (PFGs). From an implementation perspective, designing a unified and flexible hardware architecture for BPL decoding that supports various PFGs and code configurations presents a big challenge. In this paper, we propose the first hardware implementation of a BPL decoder for polar codes and overcome the implementation challenge by applying a hardware-friendly algorithm that generates flexible permutations on-the-fly. First, we derive the graph selection gain and provide a sequential generation (SG) algorithm to obtain a near-optimal PFG set. We further prove that any permutation can be decomposed into a combination of multiple fixed routings, and we design a low-complexity permutation network to satisfy the decoding schedule. Our BPL decoder not only has a low decoding latency by executing the decoding and permutation generation in parallel, but also supports an arbitrary list size without any area overhead. Experimental results show that, for length-1024 polar codes with a code rate of one-half, our BPL decoder with 32 PFGs has a similar error-correcting performance to SCL with a list size of 4 and achieves a throughput of 25.63 Gbps and an area efficiency of 29.46 Gbps/mm2^{2}2 at SNR=4.0dB, which is 1.82×\times× and 4.33×\times× faster than the state-of-the-art BP flip and SCL decoders,~respectively
Belief propagation (BP) decoding for polar codes has been extensively studied because of its inherent parallelism. However, its performance remains inferior to that of successive cancellation list decoding (SCL) due to the structure of the decoding graph. To improve the block error rate (BLER) performance, the BP correction (BPC) decoding, a post-processing scheme that corrects prior knowledge of the identified code bit, improves convergence by executing additional iterations on the failed BP decoder. Moreover, the BPC decoder demonstrates a better decoding performance than the BP-based bit-flipping decoder. Nevertheless, the additional decoding attempts lead to increased latency. In this article, a modified BPC decoder is proposed to reduce the number of decoding attempts by redefining the correction rules. A new metric is designed to effectively identify the corrected location. Numerical results show that the proposed modified BPC decoder achieves a slight improvement in BLER compared with the original BPC, with a dramatic reduction in average complexity. Furthermore, a higher-order version, named MBPC-Ω, is extended to further improve the performance, where the Ω is the maximum correction order. Numerical results show that the higher-order modified BPC achieves a similar BLER performance to existing multiple bit-flipping BP decoders but has around half the latency overhead. In addition, the proposed MBPC-2 decoder performs better than the cyclic redundancy check-aided SCL (CA-SCL) decoder with list size 4 and is slightly worse than the CA-SCL with list size 8 in high signal-to-noise ratio (SNR) regions but with significant decoding latency reduction.
Polar codes have become the channel coding scheme for control channel of enhanced mobile broadband in the 5G communication systems. Belief propagation (BP) decoding of polar codes has advantages of low decoding latency and high parallelism but achieves worse bit error ratio (BER) performance compared with the successive cancellation list (SCL) decoding scheme. In this paper, an improved BP list (IBPL) decoding algorithm is proposed with comparable BER performance to SCL algoritm. Firstly, the optimal permuted factor graph is analyzed for polar codes, which improves the performance of the BP decoder without path extension. Furthermore, based on the optimal graph, the bit metric and decoding path metric are proposed to extend and prune the decoding path. The proposed IBPL decoder is focused on not only the permutation of polar codes but also the reliabilities of decoded codewords during each iteration of BP decoding, which has a more accurate decoding path list. The simulation results show that the proposed IBPL decoder improves the BER performance compared with the original BP decoder significantly, and can approach the performance of the SCL decoder at low signal to noise ratio regions.
A polar code decoder based on the belief propagation algorithm is desirable because of the potentially low latency and its suitability for parallel execution on multicore and SIMD processors. However, current state-of-the-art algorithms require many iterations to achieve comparable bit and frame error rate compared to successive cancellation algorithms. Also, the current state-of-the-art belief propagation algorithms have a high computational complexity compared to successive cancellation. In this paper we present an enhanced belief propagation algorithm, in which parts of the computations are altered to reduce the negative effect of the short cycles in the polar code factor graph. Our proposed algorithm has a gain of approx+0.4mathbf{dB} in both frame and bit error rate compared to successive cancellation and a gain of approx+0.16mathbf{dB} and approx+0.13mathbf{dB} at a frame and bit error rate of 10-3 respectively, compared to belief propagation. Also, the maximum number of iterations of our algorithm is reduce to 0.6cdot I_{max}. As a result, the latency is up to approx 11 times lower compared to successive cancellation and up to approx 1.8 times lower compared to the current state-of-the-art belief propagation polar code algorithm. Furthermore, the reduction in the maximum iteration count results in a lower power consumption after implementation.