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Article summary:
1. Presents a deterministic algorithm for computing the entire weight distribution of polar codes.
2. Derives an efficient recursive procedure to compute the weight distribution that arises in successive cancellation decoding of polar codes along any decoding path.
3. Proves that a subgroup of LTA acts transitively on certain subsets of decreasing monomial codes, thereby drastically reducing the number of polar cosets that need to be evaluated.
Article analysis:
The article is reliable and trustworthy as it provides a detailed description of the algorithm for computing the weight distribution of polar codes, and presents evidence to support its claims. The authors provide an efficient recursive procedure to compute the weight distribution, which solves an open problem recently posed by Polyanskaya, Davletshin, and Polyanskii. Furthermore, they prove that a subgroup of LTA acts transitively on certain subsets of decreasing monomial codes, which reduces the complexity of their algorithm significantly. The article does not appear to have any biases or one-sided reporting; all claims are supported with evidence and counterarguments are explored where necessary. There is no promotional content or partiality present in the article either; all possible risks are noted and both sides are presented equally throughout.