# Factorization of Joint Probability Mass Functions into Parity Check Interactions

2009-07-03
Bayramoglu, Muhammet Fatih
Yılmaz, Ali Özgür
We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors an d factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity chec k 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 PMF s and orthogonal projections for obtaining this factorization.

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Citation Formats
M. F. Bayramoglu and A. Ö. Yılmaz, “Factorization of Joint Probability Mass Functions into Parity Check Interactions,” 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36636. 