2015/02/10 by Muhammet Fatih Bayramoglu, Bayramoglu, Muhammet Fatih
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Algorithms and Data Compression #Bayesian Modeling and Causal Inference #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Neural Networks and Applications #Probability (math.PR) #cs.IT #math.IT #math.PR
paper · pdf · doi:10.48550/arxiv.1502.02940
PhD Dissertation, 123 pages
arxiv created 2015/02/10 · openalex publication_date 2015/02/10 · arxiv updated 2015/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special for two reasons. First, it reveals the algebraic relations between the involved random variables. Second, it determines the conditional independence relations between the random variables. Due to the first property of the resulting factorization, it can be shown that channel decoders can be employed in the solution of probabilistic inference problems other than decoding. This approach might lead to new probabilistic inference algorithms and new hardware options for the implementation of these algorithms. An example of new inference algorithms inspired by the idea of using channel decoder for other inference tasks is a multiple-input multiple-output (MIMO) detection algorithm which has a complexity of the square-root of the optimum MIMO detection algorithm.