Learning to Denoise and Decode: A Novel Residual Neural Network Decoder for Polar Codes

Dou Li; Hongfei Zhu; Yuping Zhao; Zhiwei Cao

REVIEW 2 major objections 6 minor 24 references

Learning to Denoise and Decode: A Novel Residual Neural Network Decoder for Polar Codes

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Adding a residual-learning denoiser before a neural decoder improves BER for a short polar code over a plain neural decoder at comparable latency.

desk verdict A genuinely new but small combination—residual denoising plus neural polar decoding—with a real BER gain at N=16, undermined by an unauditable latency comparison that the paper's own motivation rests on. read the letter →

arxiv 1908.00460 v1 pith:ROEG7QTR submitted 2019-08-01 eess.SP cs.ITmath.IT

Zhiwei Cao , Hongfei Zhu , Yuping Zhao , Dou Li This is my paper · ORCID

classification eess.SPcs.ITmath.IT

keywords polardecoderdecodingnetworkneuralresidualcodeslearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Polar codes are error-correcting codes used in 5G control channels. A classic decoder called SC works step by step, which is slow. Neural network decoders, or NNDs, can decode in one shot by mapping the received signal to bits using a trained network, but they were less accurate than SC.

This paper adds a denoiser before the decoder. The denoiser is a small neural network that learns to subtract noise from the received signal. Instead of directly mapping the noisy signal to bits, the network first cleans the signal, and then the decoder reads the cleaned signal. Both parts are trained together using a loss that penalizes both denoising error and bit errors.

The authors tested three neural network types (MLP, CNN, RNN) as the denoiser and decoder on a tiny polar code of length 16 with 8 information bits. The best result, an MLP version, got about 0.2 dB better bit-error rate than a plain NND and came close to SC, while supposedly running over 100 times faster than SC. However, the latency comparison lacks implementation details, and the paper does not test whether a simpler denoiser would work as well.

Extended reading notes

Core claim

The proposed RNND, which inserts a residual-learning denoiser before the neural decoder and trains both jointly with the multi-task loss L = L_denoise + L_decode (Eq. 6), achieves better BER than the corresponding NND under comparable latency, with MLP-RNND approaching SC performance and claimed to run over 100 times faster than SC (Fig. 8 and Fig. 9).

Load-bearing premise

The computation-time comparison in Section V-D (Fig. 9) assumes that the SC algorithm, NNDs, and RNNDs are implemented and measured under comparable hardware and optimization conditions, but the paper gives no details on platform, software, or whether SC is optimized. If the SC implementation is naive or runs on slower hardware, the claimed >100x speedup of MLP-RNND over SC and the 'comparable latency' between NND and RNND would not be established, undermining the paper's low-latency motivation.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the actual contribution is a modest but real one—putting a residual-learning denoiser in front of a neural polar decoder and training the two jointly with a sum of denoising and decoding losses. For the tested case (N=16, R=1/2, AWGN), the BER curves in Fig. 8 show a few tenths of a dB gain over a plain NND at BER 1e-4, and the comparison against equal-parameter NNDs is the right way to isolate the effect. That part is credible.

Where the paper falls down is the latency claim. The abstract and conclusion sell the method on low latency, but the entire '100x faster than SC' and 'comparable latency' argument rests on Fig. 9, which has zero measurement detail: no hardware model, no framework, no SC implementation notes, no batching information, no trial count. That is a load-bearing missing protocol, not a minor omission. If the SC reference is a naive CPU loop and the neural nets are batched on a GPU, the speedup claims are meaningless. This is the same point the stress-test note makes, and reading the paper confirms it.

Other soft spots: no error bars or multiple-seed statistics, no baseline with a non-residual denoiser (so you cannot tell how much of the gain comes from residual learning vs. just adding a trainable front-end), and the scope is genuinely narrow—short polar codes only, with no evidence the approach scales. The paper also has a small typo in Section V-B where a test-SNR value is missing, and the PDF figure is more illustrative than quantitative. These are minor next to the latency issue.

The citation pattern looks fine; the authors build on the NND literature and the denoising literature without overclaiming novelty. The central BER result is plausible and the multi-task loss is clean.

Who is this for: someone working on neural decoding of short codes who wants a quick, cheap way to squeeze out a bit of performance. It is not going to change the landscape for practical polar decoding. It deserves a serious referee only if the latency comparison can be made reproducible—otherwise the paper's main motivation is unverifiable. I would accept it for peer review with major revisions, specifically asking for the measurement protocol, repeated trials, and an ablation with a plain (non-residual) denoiser. That is enough to turn a plausible simulation study into a solid one.

Referee Report

2 major / 6 minor

Summary. The paper proposes a residual neural network decoder (RNND) for short polar codes. The RNND inserts a residual-learning denoising module before a neural network decoder and trains both jointly with a multi-task loss L = L_denoise + L_decode (Eq. 6). Using (16,8) polar codes with BPSK over AWGN, the authors compare MLP-, CNN-, and RNN-based RNNDs against their NND counterparts and against successive cancellation (SC). Numerical results show that each RNND improves BER relative to its NND counterpart, with MLP-RNND approaching SC performance, and the paper claims that MLP-RNND runs more than 100 times faster than SC.

Significance. If the reported results hold, this is a modest but useful empirical contribution to neural decoding of short polar codes. The architecture is simple, the comparison across three neural-network families is informative, and the parameter-matched NND baselines are a fair design choice. The paper does not contain mathematical derivations or machine-checked proofs, and the performance claims are based on simulations only; nevertheless, the proposed loss and architecture are concrete and falsifiable, and the reported BER gains are consistent across all three architecture families. The main weakness is that the paper's key motivation, low latency, rests on a computation-time comparison that currently lacks sufficient measurement detail to be verified.

major comments (2)

[V-D, Fig. 9] The computation-time comparison that underlies the abstract's low-latency claim is not auditable. The manuscript does not report the CPU/GPU model, the software framework, the SC implementation details (language, optimizations, whether a standard or optimized version was used), the batch size, the number of repeated trials, or whether neural-network inference was batched while SC was run serially. As written, the claimed 'more than 100 times faster' figure and the statement that RNNDs run only 'slightly slower' than NNDs cannot be reproduced or verified, and the comparison may not be apples-to-apples. Please document the measurement protocol and provide absolute timings for all decoders on the same platform.
[V-C, Fig. 8] The BER curves in Fig. 8 appear to be single simulation traces without error bars, confidence intervals, or multiple training seeds. Since the headline gain of MLP-RNND over MLP-NND is about 0.2 dB at BER 10^-4 and the curves are close in some SNR regions, the authors should report the number of test blocks and either error bars or mean plus/minus standard deviation over several independent training runs, so that the reader can assess whether the reported gains are statistically meaningful.

minor comments (6)

[IV-C] In the sentence 'Since Ldenoise andLdenoise are both continuous and differentiable everywhere', the second loss should be Ldecode; the current text contains a typographical error.
[IV-D] In the training procedure, 'Leaning rate' should be 'Learning rate'.
[V-B] The sentence describing Fig. 6 contains 'test-SNR = dB', which appears to be missing a value; please specify the SNR value and describe how the SNR after denoising is computed.
[V-D] The statement that 'RNNDs run slightly slower than NNDs' is not quantified; please give the measured inference times so that the reader can judge the magnitude of the difference.
[VI] The concluding claim that the RNND can be extended to longer code lengths is speculative, because no experiments or training-complexity analysis for longer polar codes are provided; please temper or support this statement.
[III] There is a typo in 'trainsmitted'; it should be 'transmitted'.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. It relies on standard channel and coding math plus the domain assumption that neural networks can learn decoding rules for short codes. The main choices that are not derived are the training SNR, the equal loss weighting, and the architecture sizes.

free parameters (4)

train-SNR = 0 dB
Training SNR chosen following [10]; affects the noise level the denoiser and decoder learn.
loss weighting (Ldenoise + Ldecode) = 1:1 ratio
The multi-task loss in Eq. 6 weights denoising and decoding equally without justification or tuning.
architecture sizes (MLP/CNN/RNN layers and nodes) = e.g., 3 layers 128-64-32 for MLP
Chosen by hand; the paper states similar parameter counts for fairness but does not explain the choices.
learning rate, momentum, batch size, epochs = 0.001, 0.99, 64, 216
Standard training choices; not derived from theory.

assumptions (5)

standard math Polar codes are capacity-achieving for symmetric B-DMCs (Arikan 2009)
Cited as motivation; not used in the derivation.
domain assumption A neural network can learn to decode a given code to near-MAP performance for short block lengths
Basis of NND from [10]; the paper relies on this to build its decoder.
domain assumption Residual learning can effectively denoise signals
Imported from image denoising literature [16] and applied to 1D codewords.
domain assumption The AWGN channel model with known SNR at test time matches the training distribution except for noise level
Required for the trained network to generalize from train-SNR 0 dB to test SNR 0-7 dB.
standard math The BPSK mapping s_i = 1 - 2x_i and the polar code generator matrix G_N are correctly implemented
Standard implementation; no code or verification provided.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Learning to Denoise and Decode: A Novel Residual Neural Network Decoder for Polar Codes." pith.science (2026). https://pith.science/paper/ROEG7QTR

@misc{pith2026190800460,
  author       = {Pith},
  title        = {Pith review of: Learning to Denoise and Decode: A Novel Residual Neural Network Decoder for Polar Codes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ROEG7QTR}},
  note         = {Machine review of arXiv:1908.00460}
}

read the original abstract

Polar codes have been adopted as the control channel coding scheme in the fifth generation new radio (5G NR) standard due to its capacity-achievable property. Traditional polar decoding algorithms such as successive cancellation (SC) suffer from high latency problem because of their sequential decoding nature. Neural network decoder (NND) has been proved to be a candidate for polar decoder since it is capable of oneshot decoding and parallel computing. Whereas, the bit-errorrate (BER) performance of NND is still inferior to that of SC algorithm. In this paper, we propose a residual neural network decoder (RNND) for polar codes. Different from previous works which directly use neural network for decoding symbols received from the channel, the proposed RNND introduces a denoising module based on residual learning before NND. The proposed residual learning denoiser is able to remove remarkable amount of noise from received signals. Numerical results show that our proposed RNND outperforms traditional NND with regard to the BER performance under comparable latency.

Figures

Figures reproduced from arXiv: 1908.00460 by the authors.

**Figure 3.** Diagram of long short-time memory (LSTM). [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗

**Figure 4.** Diagram of the residual learning block. H(x) corresponds to the stacked weight layers with Relu non-linearity. shortcut connections [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗

Figures from the paper (5 more)

**Figure 5.** Figure 5: The system model in this paper. Residual learning denoiser and neural network decoder make up the architecture of the proposed RNND. The [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

**Figure 7.** Figure 7: The PDF of signals before and after denoising of the MLP-RNND [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

**Figure 8.** Figure 8: The BER performance comparison of NNDs, proposed RNNDs and [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]

**Figure 9.** Figure 9: It is worthwhile mentioning that although there exists [PITH_FULL_IMAGE:figures/full_fig_p005_9.png]

**Figure 9.** Figure 9: The computation time comparison of NNDs, proposed RNNDs and [PITH_FULL_IMAGE:figures/full_fig_p006_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

24 extracted references · 17 canonical work pages

[1]

Channel polarization: A method for constructing capacity- achieving codes for symmetric binary-input memoryless channels,

E. Arikan, “Channel polarization: A method for constructing capacity- achieving codes for symmetric binary-input memoryless channels,”IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051–3073, July 2009

work page 2009
[2]

List decoding of polar codes,

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Transactions on Information Theory , vol. 61, no. 5, pp. 2213–2226, May 2015

work page 2015
[3]

List successive cancellation decoding of polar codes,

K. Chen, K. Niu, and J. R. Lin, “List successive cancellation decoding of polar codes,” Electronics Letters, vol. 48, no. 9, pp. 500–501, April 2012

work page 2012
[4]

Stack decoding of polar codes,

K. Niu and K. Chen, “Stack decoding of polar codes,” Electronics Letters, vol. 48, no. 12, pp. 695 –697, June 2012

work page 2012
[5]

Crc-aided decoding of polar codes,

——, “Crc-aided decoding of polar codes,” IEEE Communications Letters, vol. 16, no. 10, pp. 1668–1671, October 2012

work page 2012
[6]

Deep residual learning for image recognition,

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2016, pp. 770–778

2016
[7]

Sequence to Sequence Learning with Neural Networks,

I. Sutskever, O. Vinyals, and Q. V . Le, “Sequence to Sequence Learning with Neural Networks,” arXiv e-prints, p. arXiv:1409.3215, Sep 2014

arXiv 2014
[8]

Deepdriving: Learning affordance for direct perception in autonomous driving,

C. Chen, A. Seff, A. Kornhauser, and J. Xiao, “Deepdriving: Learning affordance for direct perception in autonomous driving,” in 2015 IEEE International Conference on Computer Vision (ICCV) , Dec 2015, pp. 2722–2730

work page 2015

Show all 24 references

[9]

Automatic differentiation in PyTorch,

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, 2017

2017
[10]

On deep learning- based channel decoding,

T. Gruber, S. Cammerer, J. Hoydis, and S. t. Brink, “On deep learning- based channel decoding,” in 2017 51st Annual Conference on Informa- tion Sciences and Systems (CISS) , March 2017, pp. 1–6

2017
[11]

Decoding of polar code by using deep feed-forward neural networks,

J. Seo, J. Lee, and K. Kim, “Decoding of polar code by using deep feed-forward neural networks,” in 2018 International Conference on Computing, Networking and Communications (ICNC) , March 2018, pp. 238–242

2018
[12]

Activation functions of deep neural networks for polar decoding applications,

——, “Activation functions of deep neural networks for polar decoding applications,” in 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC) , Oct 2017, pp. 1–5

2017
[13]

Deep learning for polar codes over ﬂat fading channels,

A. Irawan, G. Witjaksono, and W. K. Wibowo, “Deep learning for polar codes over ﬂat fading channels,” in 2019 International Conference on Artiﬁcial Intelligence in Information and Communication (ICAIIC) , Feb 2019, pp. 488–491

2019
[14]

Performance evaluation of channel decoding with deep neural networks,

W. Lyu, Z. Zhang, C. Jiao, K. Qin, and H. Zhang, “Performance evaluation of channel decoding with deep neural networks,” in 2018 IEEE International Conference on Communications (ICC) , May 2018, pp. 1–6

2018
[15]

A uniﬁed deep learning based polar-ldpc decoder for 5g communication systems,

Y . Wang, Z. Zhang, S. Zhang, S. Cao, and S. Xu, “A uniﬁed deep learning based polar-ldpc decoder for 5g communication systems,” in 2018 10th International Conference on Wireless Communications and Signal Processing (WCSP) , Oct 2018, pp. 1–6

2018
[16]

Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising,

K. Zhang, W. Zuo, Y . Chen, D. Meng, and L. Zhang, “Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising,” IEEE Transactions on Image Processing , vol. 26, no. 7, pp. 3142–3155, July 2017

2017
[17]

On the difﬁculty of training recurrent neural networks,

R. Pascanu, T. Mikolov, and Y . Bengio, “On the difﬁculty of training recurrent neural networks,” in International conference on machine learning, 2013, pp. 1310–1318

2013
[18]

Long short-term memory,

J. Schmidhuber and S. Hochreiter, “Long short-term memory,” Neural Computing, vol. 9, no. 8, pp. 1735–1780, 1997

1997
[19]

Gated feedback recurrent neural networks,

J. Chung, C. Gulcehre, K. Cho, and Y . Bengio, “Gated feedback recurrent neural networks,” in International Conference on Machine Learning, 2015, pp. 2067–2075

2015
[20]

Deep residual learning for image recognition,

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition , 2016, pp. 770–778

2016
[21]

Large-scale machine learning with stochastic gradient de- scent,

L. Bottou, “Large-scale machine learning with stochastic gradient de- scent,” in Proceedings of COMPSTAT’2010. Springer, 2010, pp. 177– 186

2010
[22]

Adam: A method for stochastic optimization,

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 , 2014

2014 arXiv
[23]

An artiﬁcial neural net viterbi decoder,

Xiao-An Wang and S. B. Wicker, “An artiﬁcial neural net viterbi decoder,” IEEE Transactions on Communications , vol. 44, no. 2, pp. 165–171, Feb 1996

1996
[24]

A theoretical analysis of feature pooling in visual recognition,

Y .-L. Boureau, J. Ponce, and Y . LeCun, “A theoretical analysis of feature pooling in visual recognition,” in Proceedings of the 27th international conference on machine learning (ICML-10) , 2010, pp. 111–118

2010

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Channel polarization: A method for constructing capacity- achieving codes for symmetric binary-input memoryless channels,

E. Arikan, “Channel polarization: A method for constructing capacity- achieving codes for symmetric binary-input memoryless channels,”IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051–3073, July 2009

work page 2009

[2] [2]

List decoding of polar codes,

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Transactions on Information Theory , vol. 61, no. 5, pp. 2213–2226, May 2015

work page 2015

[3] [3]

List successive cancellation decoding of polar codes,

K. Chen, K. Niu, and J. R. Lin, “List successive cancellation decoding of polar codes,” Electronics Letters, vol. 48, no. 9, pp. 500–501, April 2012

work page 2012

[4] [4]

Stack decoding of polar codes,

K. Niu and K. Chen, “Stack decoding of polar codes,” Electronics Letters, vol. 48, no. 12, pp. 695 –697, June 2012

work page 2012

[5] [5]

Crc-aided decoding of polar codes,

——, “Crc-aided decoding of polar codes,” IEEE Communications Letters, vol. 16, no. 10, pp. 1668–1671, October 2012

work page 2012

[6] [6]

Deep residual learning for image recognition,

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2016, pp. 770–778

2016

[7] [7]

Sequence to Sequence Learning with Neural Networks,

I. Sutskever, O. Vinyals, and Q. V . Le, “Sequence to Sequence Learning with Neural Networks,” arXiv e-prints, p. arXiv:1409.3215, Sep 2014

arXiv 2014

[8] [8]

Deepdriving: Learning affordance for direct perception in autonomous driving,

C. Chen, A. Seff, A. Kornhauser, and J. Xiao, “Deepdriving: Learning affordance for direct perception in autonomous driving,” in 2015 IEEE International Conference on Computer Vision (ICCV) , Dec 2015, pp. 2722–2730

work page 2015