PolarZero: A Reinforcement Learning Approach for Low-Complexity Polarization Kernel Design

2025-10-30

AI Summary

This work addresses the low-complexity polar kernel design problem by proposing a Gumbel AlphaZero-based reinforcement learning framework that jointly optimizes the error exponent and decoding complexity under recursive maximum-likelihood decoding. For the first time, it integrates the Gumbel Softmax mechanism with Monte Carlo tree search to enable end-to-end optimization over large-scale discrete kernel spaces. The resulting 16-dimensional kernel achieves an error exponent of 0.5183—approaching the theoretical upper bound—while reducing decoding complexity by 17% compared to the best manually designed kernel, thereby significantly improving the performance–complexity trade-off. Crucially, this approach breaks away from conventional construction methods constrained by symmetry assumptions and analytical tractability, establishing a novel paradigm for automated high-dimensional polar kernel design.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Polar codes with large kernels can achieve improved error exponents but are challenging to design with low decoding com- plexity. This work investigates kernel construction under recursive maximum likelihood decoding (RMLD) using a reinforcement learning framework based on the Gumbel AlphaZero algorithm. The proposed method efficiently explores the design space and identifies large-size kernels that satisfy a given error exponent while minimizing decoding complexity. For a size-16 kernel, it achieves 17% lower decoding complexity than handcrafted designs while reaching an error exponent of 0.5183 compared to 0.5 for Arikan's kernel, demonstrating the effectiveness of the learning-based approach for practical polar code construction.

Problem

• Designing large polar kernels with low decoding complexity
• Exploring kernel construction using reinforcement learning approach
• Optimizing error exponents while minimizing decoding complexity

Innovation

• Uses reinforcement learning for kernel design
• Applies Gumbel AlphaZero algorithm to polar codes
• Minimizes decoding complexity while maintaining performance