Efficient analysis and maximization of SCL decoding performance

Develop an efficient mathematical tool for analyzing and maximizing the successive cancellation list decoding performance of polar codes for practical list sizes, specifically 4 ≤ L ≤ 16.

Background

The paper designs extended polar codes by selecting intermediate or coded nodes whose values are repeated and transmitted through transmission holes created by puncturing. The extension pattern is optimized for successive cancellation list decoding (SCLD) performance using reinforcement learning because the authors state that direct analytical optimization is unavailable for practical list sizes.

An efficient analytical characterization would provide a principled alternative or complement to reinforcement-learning-based design. In the proposed method, node selection is instead guided by density-evolution analysis of reliability propagation and by empirical SCLD rewards, rather than by an exact mathematical measure of each node’s contribution to SCLD performance.

References

However, to the best of our knowledge, no efficient mathematical tool exists to analyze and maximize the SCLD performance for a practical list size (i.e., $4 \le L \le 16$).

— Design of Polar Codes with Puncturing and Extending  (2609.26301 - Han et al., 22 Sep 2026) in Section 1, Introduction; discussed again in Section 4.3, “Multi-stage Learning and State Reduction”