Reliability vs Stability: Polar Code Construction Based on Varentropy Under the Successive Cancellation List Decoding

Successive cancellation list decoding (SCL) is a high-performance decoding algorithm designed for polar codes. To date, a comprehensive criterion for the optimal construction of polar codes under the SCL decoding remains elusive. We consider varentropy as a measure of synthetic channel stability and introduce it into the construction of polar codes under the SCL decoding. This is referred to as the RM-Var construction. The encoding of polar codes is generally dependent on the channel, while varentropy is a statistical characteristic purely based on channel transition probabilities. Introducing varentropy into the construction aligns better with the characteristics of polar codes. In certain scenarios, the RM-Var construction demonstrates superior performance compared with traditional constructions, suggesting that we may have identified a new criterion for the construction of polar codes under the SCL decoding.