Efficient Majority-Logic Decoding of Short-Length Reed-Muller Codes at Information Positions
Year: 2013
Type: article
Abstract: Short-length Reed-Muller codes under majority-logic decoding are of particular importance for efficient hardware implementations in real-time and embedded systems. This paper significantly improves Chen's two-step majority-logic decoding method for binary Reed-Muller codes RM(r,m), r ≤ m/2, if - systematic encoding assumed - only errors at information positions are to be corrected. Some general results on the minimal number of majority gates are presented that are particularly good for short codes. Specifically, with its importance in applications as a 3-error-correcting, self-dual code, the smallest non-trivial example, RM(2,5) of dimension 16 and length 32, is investigated in detail. Further, the decoding complexity of our procedure is compared with that of Chen's decoding algorithm for various Reed-Muller codes up to length 210.
Authors: Peter Hauck, Michael Huber, Juliane Bertram, Dennis Brauchle, Sebastian Ziesche
Institution: University of Tübingen
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1993003751