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Factorization of Joint Probability Mass Functions into Parity Check Interactions
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Date
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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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.