A Hilbert Space of Probability Mass Functions and Applications on the Sum-Product Algorithm

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2008-09-05

Author

Bayramoglu, Muhammet Fatih
Yılmaz, Ali Özgür

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In this paper a Hilbert space structure of probability mass functions (PMF) will be presented. The tools provided by the Hilbert space, specifically the norm and the inner product, may be useful while analyzing and improving the sum-product algorithm in many aspects. Our approach provides a metric distance between PMFs and a new point of a view of the log-likelihood ratio (LLR) such that the LLR representation is nothing but a Hilbert space representation.

Subject Keywords

Hilbert space, Sum product algorithm, Distance measurement, Equations, Probability density function, Vectors, Mathematical model

URI

https://hdl.handle.net/11511/39906

DOI

https://doi.org/10.1109/turbocoding.2008.4658722

Conference Name

5th International Symposium on Turbo Codes and Related Topics

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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, “A Hilbert Space of Probability Mass Functions and Applications on the Sum-Product Algorithm,” presented at the 5th International Symposium on Turbo Codes and Related Topics, Lausanne, SWITZERLAND, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39906.