The Complete SC-invariant Affine Automorphisms of Polar Codes
Zicheng Ye, Yuan Li, Huazi Zhang, Rong Li, Jun Wang, Guiying Yan and, Zhiming Ma
TL;DR
This paper characterizes all affine automorphisms of polar codes that are invariant under successive cancellation decoding, enabling more efficient automorphism ensemble decoding by eliminating redundant automorphisms.
Contribution
It provides a necessary and sufficient condition based on matrix structure and an algorithm to identify all SC-invariant affine automorphisms for polar codes.
Findings
Identifies the complete set of SC-invariant affine automorphisms
Provides an algorithm to determine these automorphisms
Reduces redundancy in automorphism ensemble decoding
Abstract
Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders in parallel and hence has lower latency compared to that of successive cancellation list (SCL) decoding. However, some automorphisms are SC-invariant, thus are redundant in AE decoding. In this paper, we find a necessary and sufficient condition related to the block lower-triangular structure of transformation matrices to identify SC-invariant automorphisms. Furthermore, we provide an algorithm to determine the complete SC-invariant affine automorphisms under a specific polar code construction.
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Taxonomy
TopicsMultilevel Inverters and Converters · Islamic Finance and Communication · Coding theory and cryptography