Factorization of Joint Probability Mass Functions into Parity Check Interactions
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.
Cite
@article{arxiv.0901.3056,
title = {Factorization of Joint Probability Mass Functions into Parity Check Interactions},
author = {M. F. Bayramoglu and A. Özgür Yılmaz},
journal= {arXiv preprint arXiv:0901.3056},
year = {2009}
}
Comments
5 pages, 1 figures, appeared in the proceedings of ISIT 2009; Changed content, more recent version than as appeared in the proceedings