ZeroCode: On-demand Error-Correcting Code Construction from the Zero Matrix via Reinforcement Learning

2026-09-28

AI Summary

This study addresses the challenge of adapting parity-check matrices of error-correcting codes to diverse scenario-specific requirements by proposing a unified construction framework based on reinforcement learning. The matrix generation process is formulated as a discrete sequential decision-making problem, where edges are incrementally added to an all-zero matrix. An action masking mechanism is introduced to flexibly embed structural constraints, enabling the generation of code libraries across multiple complexities through a single policy rollout without retraining. Experimental results demonstrate that for (32,16) short codes at a bit error rate of $10^{-4}$, the proposed method achieves approximately 1 dB gain over existing genetic, differentiable, and classical approaches, thereby realizing on-demand design of high-performance error-correcting codes.

Abstract

Error-correcting codes (ECCs) are essential across diverse applications, from wireless communications and storage to quantum computing, yet each application imposes distinct design requirements on the parity-check matrix (PCM). To address these on-demand requirements in a unified framework, we propose ZeroCode, a reinforcement learning (RL)-based approach that constructs PCMs sequentially from the all-zero matrix. ZeroCode formulates construction as a discrete sequential decision-making problem and uses proximal policy optimization with action masking to select valid edges. ZeroCode achieves a gain of approximately 1 dB over the prior RL-based construction method at a bit error rate (BER) of $10^{-4}$ for the (32,16) code and outperforms existing genetic, differentiable, and classical code-design methods in our experiments. Beyond optimizing decoding performance, the masking mechanism allows on-demand structural constraints, such as a maximum degree, 4-cycle-free structure, and quasi-cyclic structure, to be flexibly incorporated. Moreover, a single policy rollout yields a library of PCMs with varying edge counts, offering trade-offs between decoding performance and complexity without retraining. Overall, ZeroCode addresses diverse code-design requirements within a unified framework, providing solutions with optimized decoding performance under given constraints.

Problem

• Error-correcting codes
• Parity-check matrix
• On-demand code construction
• Structural constraints
• Decoding performance

Innovation

• Reinforcement Learning
• Error-Correcting Codes
• Parity-Check Matrix
• Action Masking
• Proximal Policy Optimization