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

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