Factorization of Joint Probability Mass Functions into Parity Check Interactions

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2009-07-03

Author

Bayramoglu, Muhammet Fatih
Yılmaz, Ali Özgür

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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.

Subject Keywords

Parity check codes, Hilbert space, Decoding, Galois fields, Equations, Terminology, Helium, Sum product algorithm, Random variables

URI

https://hdl.handle.net/11511/36636

DOI

https://doi.org/10.1109/isit.2009.5205262

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Department of Electrical and Electronics Engineering, Conference / Seminar

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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.