References & Citations
Computer Science > Information Theory
Title: Enumeration of Minimum Weight Codewords of Pre-Transformed Polar Codes by Tree Intersection
(Submitted on 29 Nov 2023 (v1), last revised 26 Apr 2024 (this version, v4))
Abstract: Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this work, we propose an efficient algorithm for determining the number of minimum weight codewords of general PTPCs that eliminates all redundant visits to nodes of the search tree, thus reducing the computational complexity typically by several orders of magnitude compared to state-of-the-art algorithms. This reduction in complexity allows, for the first time, the minimum distance properties to be directly considered in the code design of PTPCs. The algorithm is demonstrated for randomly pre-transformed Reed-Muller (RM) codes and polarization-adjusted convolutional (PAC) codes. Furthermore, we design optimal polynomials for PAC codes with this algorithm, minimizing the number of minimum weight codewords.
Submission history
From: Marvin Geiselhart [view email][v1] Wed, 29 Nov 2023 16:19:34 GMT (141kb)
[v2] Fri, 8 Dec 2023 12:30:50 GMT (114kb)
[v3] Fri, 22 Dec 2023 15:14:26 GMT (114kb)
[v4] Fri, 26 Apr 2024 09:02:33 GMT (115kb)
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