A Hilbert space of probability mass functions and applications on the sum-product algorithm | IEEE Conference Publication | IEEE Xplore

A Hilbert space of probability mass functions and applications on the sum-product algorithm


Abstract:

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 inne...Show More

Abstract:

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.
Date of Conference: 01-05 September 2008
Date Added to IEEE Xplore: 24 October 2008
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Conference Location: Lausanne, Switzerland

I. Introduction

The sum-product algorithm has been extremely popular in the communication community since the invention of turbo codes [3], [4], [5]. The sum-product algorithm elegantly solves the marginalized product density problem in a message passing fashion. The messages passed during the sum product algorithm (beliefs) are in fact probability density functions (PDF). Therefore, representation of the PDFs is crucial for the sum-product algorithm.

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