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Nested Construction of Polar Codes via Transformers

Sravan Kumar Ankireddy, S Ashwin Hebbar, Heping Wan, Joonyoung Cho, Charlie Zhang

TL;DR

The paper tackles the challenge of constructing polar codes that remain effective across decoders and channel conditions by formulating nested polar-code design as a sequential decision problem solvable with a transformer-based policy. By predicting the next information index given previously selected indices and optimizing a BLER-based reward across rates, the authors produce nested codes that adapt to varying rates and channels, including non-AWGN environments. Key contributions include a concrete RL-based framework with a transformer encoder and positional encoding, a nested objective across rates, and empirical gains over the 5G-NR universal sequence and DE/GA baselines, especially under Rayleigh fading. The approach offers a data-driven, rate-flexible path for practical polar-code design with potential extensions to PAC codes and end-to-end neural decoding.

Abstract

Tailoring polar code construction for decoding algorithms beyond successive cancellation has remained a topic of significant interest in the field. However, despite the inherent nested structure of polar codes, the use of sequence models in polar code construction is understudied. In this work, we propose using a sequence modeling framework to iteratively construct a polar code for any given length and rate under various channel conditions. Simulations show that polar codes designed via sequential modeling using transformers outperform both 5G-NR sequence and Density Evolution based approaches for both AWGN and Rayleigh fading channels.

Nested Construction of Polar Codes via Transformers

TL;DR

The paper tackles the challenge of constructing polar codes that remain effective across decoders and channel conditions by formulating nested polar-code design as a sequential decision problem solvable with a transformer-based policy. By predicting the next information index given previously selected indices and optimizing a BLER-based reward across rates, the authors produce nested codes that adapt to varying rates and channels, including non-AWGN environments. Key contributions include a concrete RL-based framework with a transformer encoder and positional encoding, a nested objective across rates, and empirical gains over the 5G-NR universal sequence and DE/GA baselines, especially under Rayleigh fading. The approach offers a data-driven, rate-flexible path for practical polar-code design with potential extensions to PAC codes and end-to-end neural decoding.

Abstract

Tailoring polar code construction for decoding algorithms beyond successive cancellation has remained a topic of significant interest in the field. However, despite the inherent nested structure of polar codes, the use of sequence models in polar code construction is understudied. In this work, we propose using a sequence modeling framework to iteratively construct a polar code for any given length and rate under various channel conditions. Simulations show that polar codes designed via sequential modeling using transformers outperform both 5G-NR sequence and Density Evolution based approaches for both AWGN and Rayleigh fading channels.
Paper Structure (14 sections, 6 equations, 8 figures)

This paper contains 14 sections, 6 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation and Background
  3. Polar codes
  4. Polar Code Construction
  5. Nested Construction using sequence modeling
  6. Sequential modeling for Polar Codes
  7. Related Work
  8. Results
  9. Joint Optimization for a target BLER
  10. Optimization for a target rate
  11. Effect of permutation invariant representation
  12. Conclusion and Remarks
  13. Transformer model
  14. Architecture and Training.

Figures (8)

  • Figure 1: Encoding of (8,4) Polar code with frozen nodes set to "$0$"
  • Figure 2: Predicting the $k^{\text{th}}$ information position using the first $k-1$ predictions via transformer model.
  • Figure 3: AWGN channel under CA-SCL decoder with list size 8 : Our method shows considerable SNR gain over the 5G-NR sequence and small gains over li2021learning.
  • Figure 4: Rayleigh fading channel under CA-SCL decoder with list size 8: Our method shows considerable SNR-gain over the 5G-NR sequence and baselines at target BLER 0.01.
  • Figure 5: BLER performance in AWGN channel for $(64,16)$ code under CA-SCL decoder with list size 8: For a target rate, our method achieves gains of 0.2-0.3 dB over the 5G-NR sequence and baselines.
  • ...and 3 more figures