2019/04/26 by Yuta Sakai, Ken-ichi Iwata, Hiroshi Fujisaki · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Alphabet #Coding theory and cryptography #DNA and Biological Computing #Erasure #Error Correcting Code Techniques #Lattice (music) #Polar #Polarization (electrochemistry) #cs.IT #math.IT
paper · pdf · doi:10.1109/isit.2019.8849487
12 pages, 1 figure, a short version has been accepted by the 2019 IEEE International Symposium on Information Theory (ISIT2019)
arxiv created 2019/04/26 · openalex created_date 2019/05/03 · openalex publication_date 2019/07/01 · arxiv updated 2020/08/24 · openalex updated_date 2026/08/05
Polar transforms are central operations in the study of polar codes. This paper examines polar transforms for non-stationary memoryless sources on possibly infinite source alphabets. This is the first attempt of source polarization analysis over infinite alphabets. The source alphabet is defined to be a Polish group, and we handle the Arikan-style two-by-two polar transform based on the group. Defining erasure distributions based on the normal subgroup structure, we give recursive formulas of the polar transform for erasure distributions. We then show concrete examples of multilevel source polarization with countably infinite levels when the group is locally cyclic. We derive this result via elementary techniques in lattice theory.