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Työväentutkimus Vuosikirja

5G Polar Codes: ML-Assisted Decoding Performance Comparison on GPUs

Anton Bogun

Published Sep 10, 2026• 0 citations
OpenAlex

Abstract

Polar code decoding is an algorithmic challenge that is highly sensitive to the latency and throughput. It is used in 5G NR control channels and demands good noise decoding perfor- mance. Decoders such as successive cancellation (SC) and its list variant (SCL) achieve good bit error rates (BER) throughout the signal-to-noise ratio (SNR) regimes, but suffer from high latency and challenges in parallel implementation due to their sequential nature. The belief propagation (BP) decoder is an alternative representation of the polar graph, which allows parallel decoding over the whole codeword, but requires multiple iterations to reach acceptable BER. The hardware-friendly min-sum (MS) algorithmic simplification uses cheap instructions instead of expensive transcendental operations for higher throughput and lower latency, but further negatively impacts the noise decoding performance. This thesis considers the normalized variation of min-sum (NMS), which adds trainable scales per edge in the BP graph, applied to the 5G N=128 rate 1/2 polar code. The weights are trained by treating the unrolled 5 iteration BP graph as a neural network, which achieves a better-or- equal noise performance compared to the true BP decoder, a 0.5 dB average improvement over the untrained MS, and a 5x lower BER than true BP at 6 dB SNR, making the performance roughly comparable to SC in high SNR regions. These improvements are implemented as a single optimized GPU kernel with further optimiza- tions for better throughput, and run on an NVIDIA H100 GPU. The final achieved throughput peaks at 181 million codewords per second (11.6 information Gbit/s), which is around 25x the throughput of the XLA-compiled Sionna framework running the same decoder, and around 190x of a 192-thread CPU implementation.

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Polar code decoding is an algorithmic challenge that is highly sensitive to the latency and throughput. It is used in 5G NR control channels and demands good noise decoding perfor- mance. Decoders such as successive cancellation (SC) and its list variant (SCL) achieve good bit error rates (BER) throughout the signal-to-noise ratio (SNR) regimes, but suffer from high latency and challenges in parallel implementation due to their sequential nature. The belief propagation (BP) decoder is an alternative representation of the polar graph, which allows parallel decoding over the whole codeword, but requires multiple iterations to reach acceptable BER. The hardware-friendly min-sum (MS) algorithmic simplification uses cheap instructions instead of expensive transcendental operations for higher throughput and lower latency, but further negatively impacts the noise decoding performance. This thesis considers the normalized variation of min-sum (NMS), which adds trainable scales per edge in the BP graph, applied to the 5G N=128 rate 1/2 polar code. The weights are trained by treating the unrolled 5 iteration BP graph as a neural network, which achieves a better-or- equal noise performance compared to the true BP decoder, a 0.5 dB average improvement over the untrained MS, and a 5x lower BER than true BP at 6 dB SNR, making the performance roughly comparable to SC in high SNR regions. These improvements are implemented as a single optimized GPU kernel with further optimiza- tions for better throughput, and run on an NVIDIA H100 GPU. The final achieved throughput peaks at 181 million codewords per second (11.6 information Gbit/s), which is around 25x the throughput of the XLA-compiled Sionna framework running the same decoder, and around 190x of a 192-thread CPU implementation.
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.
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
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.
Due to its high parallelism, belief propagation (BP) decoding is amenable to high-throughput applications and thus represents a promising solution for the ultra-high peak data rate required by future communication systems. To bridge the performance gap compared to the widely used successive cancellation list (SCL) decoding algorithm, BP list (BPL) decoding for polar codes extends candidate codeword exploration via multiple permuted factor graphs (PFGs) to improve the error-correcting performance of BP decoding. However, it is a significant challenge to design a unified and flexible BPL hardware architecture that supports various PFGs and code configurations. In this paper, we present the first VLSI implementation of a BPL decoder for polar codes that overcomes this implementation challenge with a hardware-friendly algorithm for on-the-fly flexible permutations. First, we introduce a sequential generation (SG) algorithm to obtain a near-optimal PFG set. Additionally, we demonstrate that any permutation can be decomposed into a combination of multiple fixed routings, and design a low-complexity permutation network to generate graphs in an on-the-fly fashion. Our BPL decoder has a low decoding latency by executing decoding and permutation generation in parallel and supports arbitrary list sizes without area overhead. Experimental results based on 28nm FD-SOI technology show that for length-1024 polar codes with a code rate of one-half, our BPL decoder with 32 PFGs exhibits similar error-correcting performance to SCL with a list size of 4 and achieves an average throughput of 25.63 Gbps and an area efficiency of 29.46 Gbps/mm2, which is 1.82× and 4.33× faster than the state-of-the-art BP flip and SCL decoders, respectively
Polar codes are the first class of error correcting codes that provably achieve the channel capacity at infinite code length. They were selected for use in the fifth generation of cellular mobile communications (5G). In practical scenarios such as 5G, a cyclic redundancy check (CRC) is concatenated with polar codes to improve their finite length performance. This is mostly beneficial for sequential successive-cancellation list decoders. However, for parallel iterative belief propagation (BP) decoders, CRC is only used as an early stopping criterion with incremental error-correction performance improvement. In this paper, we first propose a CRC-polar BP (CPBP) decoder by exchanging the extrinsic information between the factor graph of the polar code and that of the CRC. We then propose a neural CPBP (NCPBP) algorithm which improves the CPBP decoder by introducing trainable normalizing weights on the concatenated factor graph. Our results on a 5G polar code of length 128 show that at the frame error rate of 10-5and with a maximum of 30 iterations, the error-correction performance of CPBP and NCPBP are approximately 0.25 dB and 0.5 dB better than that of the conventional CRC-aided BP decoder, respectively, while introducing almost no latency overhead.
Belief propagation (BP) decoding outputs soft information and can be naturally used in iterative receivers. BP list (BPL) decoding provides comparable error-correction performance to the successive cancellation list (SCL) decoding. In this paper, we firstly introduce an enhanced code construction scheme for BPL decoding to improve its error-correction capability. Then, a GPU-based BPL decoder with adoption of the new code construction is presented. Finally, the proposed BPL decoder is tested on NVIDIA RTX3070 and GTX1060. Experimental results show that the presented BPL decoder with early termination criterion achieves above 1 Gbps throughput on RTX3070 for the code (1024, 512) with 32 lists under good channel conditions.