Factorization of Joint Probability Mass Functions into Parity Check Interactions

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Bayramoglu M. F. , Yilmaz A. O.

IEEE International Symposium on Information Theory (ISIT 2009), Seoul, South Korea, 28 June - 03 July 2009, pp.1749-1753 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/isit.2009.5205262
  • City: Seoul
  • Country: South Korea
  • Page Numbers: pp.1749-1753


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.