Pareto-Optimal Frozen Set Design for Polar Codes with Dynamic Frozen Bits under Small-List SCL Decoding

This paper focuses on low-complexity design of polar codes with high error-correction capability for 6G networks. We propose a novel frozen set design approach for polar codes with dynamic frozen bits that guarantees the best possible trade-offs between closed-form bounds on successive cancellation (SC) and maximum-likelihood (ML) decoding error probabilities, where the ML bound is the union bound parameterized by the ensemble-averaged weight distribution. To the best of our knowledge, this is the first method to generate Pareto-optimal frozen sets for these dual objectives. The low complexity of generating the frozen set Pareto front stems from our analysis of the bounds. Experimental results show that the resulting polar codes with dynamic frozen bits and near-uniformly distributed frozen bit expressions outperform the state-of-the-art codes under successive cancellation list (SCL) decoding with list sizes ranging from 2 to 16. These results suggest promising applications for next-generation wireless communication systems requiring both high reliability and computational efficiency.