Technical Program

Paper Detail

Paper Title Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions
Paper IdentifierTH3.R2.5
Authors Yuta Sakai, National University of Singapore, Singapore; Ken-ichi Iwata, University of Fukui, Japan; Hiroshi Fujisaki, Kanazawa University, Japan
Session Polarization
Location Saint Germain, Level 3
Session Time Thursday, 11 July, 14:30 - 16:10
Presentation Time Thursday, 11 July, 15:50 - 16:10
Manuscript  Click here to download the manuscript
Abstract 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 Arıkan-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.