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DeepPolar: Inventing Nonlinear Large-Kernel Polar Codes via Deep Learning
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Proposes DeepPolar codes, a non-linear neural generalization of polar codes using large (sqrt(n)-sized) neural kernels and a matching SC-style neural decoder, trained with a kernel-wise curriculum to beat Polar, RM, and KO codes in BER on AWGN.
Problem
Finding good finite-length channel codes in the short-to-medium block length regime is largely manual; existing neural codes (e.g., KO codes) are limited in rates and block lengths, and polar codes with SC/SCL decoding have limited finite-length reliability.
Approach
Replace the XOR operations of the polar Plotkin tree with neural networks and enlarge the kernel to size ell (~sqrt(n)), paired with a matching SC-like neural decoder, trained via a two-stage curriculum that first pretrains per-kernel encoder-decoder pairs on increasing message sizes and then initializes the full code from those kernels.
Key results
- DeepPolar(256,37,ell=16) outperforms KO(8,2) and classical Polar and Reed-Muller codes in BER on AWGN, with kernel sizes 16 and 32 beating KO codes.
- DeepPolar(256,37) trained on AWGN retains gains of up to 0.3 dB over Polar(256,37) on Rayleigh fading and up to 0.25 dB on bursty noise without retraining.
- DeepPolar exhibits BLER that is subpar relative to Polar codes, attributed to the BCE (BER-surrogate) training objective.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase kernel size to ℓ=16 or 32 (ablation) | DeepPolar (256,37) · AWGN | BER | Helped |
| Increase kernel size further to ℓ=64 (ablation) | DeepPolar (256,37) · AWGN | BER | Hurt |
| Use curriculum training instead of direct training (ablation) | DeepPolar · High-SNR AWGN | reliability | Helped |
| Binarize the trained code using STE and a binarization module (ablation) | DeepPolar (256,37, ℓ=16) · AWGN | BER | Hurt |
| Replace leaf SC-style neural decoders with a one-shot parallel decoder (ablation) | DeepPolar-parallel · DeepPolar (256,37) | reliability: 8x reduction in parameter count | Helped |
| Fine-tune the BCE-trained model on the BLER surrogate loss L1 (ablation) | DeepPolar · AWGN | BLER | Helped |
| Fine-tune on the BLER surrogate loss L1 (ablation) | DeepPolar · AWGN | BER | Hurt |
| Use smaller encoder and decoder hidden sizes (e=8, d=8) instead of (e=64, d=128) (ablation) | DeepPolar · AWGN, SNR -1.0 dB | BER: 5.9e-5 -> 9e-3 | Hurt |
| Use encoder and decoder hidden sizes (e=32, d=32) instead of (e=64, d=128) (ablation) | DeepPolar · AWGN, SNR -1.0 dB | BER: 5.9e-5 -> 8.3e-5 | Hurt |
| Train a dense fully connected encoder-decoder without the DeepPolar structural inductive bias (ablation) | Neural channel code · AWGN | BER | Hurt |
| Use DeepPolar-SC decoding instead of SC decoding (ablation) | Polar (256,37) · AWGN | BER | No clear effect |
Surprising findings
- Learned DeepPolar encoder's pairwise codeword distance distribution closely resembles that of a Gaussian codebook.
- Fully connected neural encoder-decoder pairs perform substantially worse than SC decoding of polar codes despite having ten times more parameters.
Limitations
- BLER is worse than polar codes because the BCE loss optimizes BER rather than BLER.
- High-SNR performance is hard to improve; gains require fine-tuning at very large batch sizes.
- Decoder complexity and parameter count are high, and the work does not optimize for low complexity.
Experimental setup
Datasets: synthetic random binary messages with simulated AWGN channel
Benchmarks: AWGN channel BER simulations for (256,37), (256,64), (256,28)
Metrics: bit error rate block error rate
Baselines: Polar codes with SC decoding Reed-Muller codes with Dumer decoding KO(8,2) codes 5G Polar codes fully connected neural code
Builds on: polar codes KO codes successive cancellation decoding
Closest papers by meaning
- Learning Linear Block Error Correction Codes (ICML 2024 · similarity 0.84)
- PolarQuant: Leveraging Polar Transformation for Key Cache Quantization and Decoding Acceleration (NeurIPS 2025 · similarity 0.82)
- SINR: Sparsity Driven Compressed Implicit Neural Representations (CVPR 2025 · similarity 0.82)
- Friendly Attacks to Improve Channel Coding Reliability (AAAI 2024 · similarity 0.82)
- Entropy-informed Decoding: Adaptive Information-Driven Branching (ICML 2026 · similarity 0.81)
- Fast Channel Simulation via Error-Correcting Codes (NeurIPS 2024 · similarity 0.81)
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