An Information-Theoretic Perspective on Successive Cancellation List Decoding and Polar Code Design

This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation (SCL) decoding implement maximum-likelihood over general binary memoryless symmetric (BMS) channels. It also provides upper and lower bounds these can be computed efficiently very long codes. For erasure channel (BEC), we provide a simple method estimate mean accurately via density evolution. The analysis shows how modify, e.g., Reed-Muller codes, improve performance when practical sizes, $L\in {[{8, 1024}]}$ , adopted. Exemplary constructions with block lengths notation="LaTeX">$N\in \{128,512\}$ outperform polar codes of 5G binary-input additive white Gaussian noise channel. is further shown there concentration around logarithm sufficiently large lengths, discrete-output BMS We probability mass functions (p.m.f.s) this logarithm, BEC, sequence modified RM an increasing length simulations, which illustrate p.m.f.s concentrate estimated mean.