2010/06/29 by Kazunori Hayashi, Hayashi, Kazunori, Yasuaki Hiraoka +1
Computer Science · Engineering · Mathematics · #37N99 #94B35 #Advanced Wireless Communication Techniques #Coding theory and cryptography #Dynamical Systems (math.DS) #Error Correcting Code Techniques #FOS: Mathematics #math.DS #msc:37N99 #msc:94B35
paper · pdf · doi:10.48550/arxiv.1006.5688
22 pages, 4 figures
arxiv created 2010/06/29 · openalex publication_date 2010/06/29 · arxiv updated 2010/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be denoted by p in the paper, is properly chosen by considering some dynamical system properties. We have two results about this approximate ML decoding. The first result proves that the order of the first nonlinear terms in the Taylor expansion is determined by the minimum distance of its dual code. As the second result, we give numerical results on bit error probabilities for the approximate ML decoding. These numerical results show better performance than that of BCH codes, and indicate that this proposed method approximates the original ML decoding very well.