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arXiv · 0901.3056

Factorization of Joint Probability Mass Functions into Parity Check Interactions

M. F. Bayramoglu·A. Özgür Yılmaz
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Abstract

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.

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M. F. Bayramoglu, A. Özgür Yılmaz. 2009-07-14. Factorization of Joint Probability Mass Functions into Parity Check Interactions. https://arxiv.org/abs/0901.3056

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