2009/01/20 by Muhammet Fatih Bayramoglu, M. F. Bayramoglu, Bayramoglu, M. F. +3
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Algorithms and Data Compression #Discrete Mathematics (cs.DM) #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR) #cs.DM #cs.IT #math.IT #math.PR
paper · pdf · doi:10.48550/arxiv.0901.3056
5 pages, 1 figures, appeared in the proceedings of ISIT 2009; Changed content, more recent version than as appeared in the proceedings
openalex publication_date 2009/01/20 · arxiv created 2009/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors and factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity check equation. In other words, marginalization of a joint PMF is equivalent to a soft decoding task as long as a finite field can be constructed over the alphabet of the PMF. In factor graph terminology this claim means that a factor graph representing such a joint PMF always has an equivalent Tanner graph. We provide a systematic method based on the Hilbert space of PMFs and orthogonal projections for obtaining this factorization.