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

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 \em 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.