Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reinforcement Learning-Aided Design of Efficient Polarization Kernels

Yi-Ting Hong, Stefano Rini, Luca Barletta

TL;DR

The paper tackles the problem of designing large-kernel polar codes that achieve high error exponents while keeping RMLD decoding complexity manageable. It introduces PolarZero, an RL-based kernel search framework built on the Gumbel AlphaZero algorithm to navigate the space of $\ell\times\ell$ kernels under PDP bounds. Results show PolarZero recovers minimal-complexity kernels up to $\ell=16$ and discovers a new size-$16$ kernel with decoding complexity close to handcrafted designs, demonstrating scalability beyond brute-force search. This data-driven approach offers a flexible tool for automated, high-performance, low-complexity polar-code design with potential applicability to even larger kernels.

Abstract

Polar codes with large kernels achieve optimal error exponents but are difficult to construct when low decoding complexity is also required. We address this challenge under recursive maximum likelihood decoding (RMLD) using a rein-forcement learning approach based on the Gumbel AlphaZero algorithm. The resulting method, PolarZero, consistently matches exhaustive search in identifying low-complexity kernels, and discovers a size-16 kernel with complexity comparable to handcrafted designs. Our results suggest that PolarZero is a scalable tool for large-kernel design, where brute-force search is no longer feasible.

Reinforcement Learning-Aided Design of Efficient Polarization Kernels

TL;DR

The paper tackles the problem of designing large-kernel polar codes that achieve high error exponents while keeping RMLD decoding complexity manageable. It introduces PolarZero, an RL-based kernel search framework built on the Gumbel AlphaZero algorithm to navigate the space of kernels under PDP bounds. Results show PolarZero recovers minimal-complexity kernels up to and discovers a new size- kernel with decoding complexity close to handcrafted designs, demonstrating scalability beyond brute-force search. This data-driven approach offers a flexible tool for automated, high-performance, low-complexity polar-code design with potential applicability to even larger kernels.

Abstract

Polar codes with large kernels achieve optimal error exponents but are difficult to construct when low decoding complexity is also required. We address this challenge under recursive maximum likelihood decoding (RMLD) using a rein-forcement learning approach based on the Gumbel AlphaZero algorithm. The resulting method, PolarZero, consistently matches exhaustive search in identifying low-complexity kernels, and discovers a size-16 kernel with complexity comparable to handcrafted designs. Our results suggest that PolarZero is a scalable tool for large-kernel design, where brute-force search is no longer feasible.
Paper Structure (19 sections, 10 equations, 3 figures, 2 tables, 2 algorithms)

This paper contains 19 sections, 10 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Polar Codes
  4. Error Exponent for Large Kernels
  5. Upper Bounds on the Partial Distance Profile (PDP)
  6. Recursive Maximum Likelihood Decoding (RMLD)
  7. RMLD Complexity Calculation
  8. Low-complexity RMLD Kernel Search Problem Formulation
  9. Proposed Approach: PolarZero
  10. Kerner Search Algorithms
  11. Brute-Force Kernel Search TroBrute24
  12. Random Agent Kernel Search
  13. PolarZero
  14. Randomized initial steps
  15. Structure of the Rewards
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Minimum, maximum, and average total rewards during training for $\ell=12$. Each iteration consists of $2000$ self-play games, with a total of $2\cdot 10^5$ episodes over $100$ iterations.
  • Figure 2: Minimum, maximum, and average total rewards during training for $\ell=16$. Each iteration consists of 2000 self-play games, with a total of $5 \cdot 10^5$ episodes over 250 iterations.
  • Figure 3: Block Error Rate (BLER) performance of polar codes using Arıkan’s kernel (SC decoding), the handcrafted kernel $G_{16}$ from handcraft_win, and the PolarZero-found kernel $A_{16}$. At each SNR, frozen bits are selected based on $10^5$ MC simulations. BLER curves are estimated using $10^5$ MC iterations per SNR.