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

Creative Commons License

Bayramoglu M. F., Yilmaz A. O.

5th International Symposium on Turbo Codes and Related Topics, Lausanne, Switzerland, 1 - 05 September 2008, pp.338-343 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/turbocoding.2008.4658722
  • City: Lausanne
  • Country: Switzerland
  • Page Numbers: pp.338-343
  • Middle East Technical University Affiliated: Yes


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.