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, Güney Kore, 28 Haziran - 03 Temmuz 2009, ss.1749-1753 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Doi Numarası: 10.1109/isit.2009.5205262
  • Basıldığı Şehir: Seoul
  • Basıldığı Ülke: Güney Kore
  • Sayfa Sayıları: ss.1749-1753
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.