Abstract
In this paper, a general transformation of binary linear block codes (BLBCs) to (possibly, multi-kernel) polar codes with dynamic frozen bits is proposed. Through a simple matrix permutation operation, a one-to-one connection between the codewords of a BLBC and its transformed polar code can be established. This transformation allows the usage of any decoding algorithm of polar codes for efficient soft decoding of BLBCs, including the powerful successive cancellation list (SCL) decoding algorithm. Simulations show that the soft SCL polar decoding of BLBCs can achieve a comparative performance to the order statistic decoding (OSD), as well as the maximum-likelihood decoding (MLD) in certain cases, with a much lower computational complexity.
Highlights
T HIS binary linear block codes (BLBC), as an important subclass of error correcting codes, have played a pivotal role in modern communications [1]
The main theme of this paper is to study the soft decoding of BLBCs with a particular focus on algebraic codes with short blocklength
In order to perform polar decoding on BLBCs, we identify a permutation matrix that transforms a BLBC to a polar code with dynamic frozen bits
Summary
T HIS binary linear block codes (BLBC), as an important subclass of error correcting codes, have played a pivotal role in modern communications [1]. In applications such as communication systems with strict latency constraints, codes with short blocklength are preferred In these particular situations, algebraic coding theory provides a powerful means to code construction with a good minimum pairwise Hamming distance among codewords. Algebraic coding theory provides a powerful means to code construction with a good minimum pairwise Hamming distance among codewords In spite of their many nice properties, most of algebraic codes suffer from a major drawback that it is difficult to exploit soft information for decoding [1], thereby lacking of soft decoding algorithms with low complexity. In order to perform polar decoding on BLBCs, we identify a permutation matrix that transforms a BLBC to a (possibly multi-kernel) polar code with dynamic frozen bits. This paper serves as a continued effort in expanding polar decoding to other classes of BLBCs
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