A Class of Transformations that Polarize Symmetric Binary-Input Memoryless Channels

2008/11/11 by Satish Babu Korada, Eren Sasoglu, Korada, Satish Babu +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cellular Automata and Applications #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.0811.1770

7 pages, 1 figure

arxiv created 2008/11/11 · openalex publication_date 2008/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A generalization of Arıkan's polar code construction using transformations of the form G^{⊗ n} where G is an ℓ × ℓ matrix is considered. Necessary and sufficient conditions are given for these transformations to ensure channel polarization. It is shown that a large class of such transformations polarize symmetric binary-input memoryless channels.

Citations

• Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels

Related

• Performance and Construction of Polar Codes on Symmetric Binary-Input Memoryless Channels
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• On the Symmetry of Polar Codes for Symmetric Binary-Input Discrete Memoryless Channels
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