Exploiting Bayesian tracking in the evaluation of Shannon information

Arnaldo Spalvieri

Politecnico di Milano
Dipartimento di Elettronica e Informazione
Via Ponzio 34/5
20133 Milano, Italy

Abstract:

Given a hidden state process with memory and a measurement process that is memoryless given the state, one has to make inference on the hidden state sequence given the measurement sequence. This activity can be performed by the so-called Bayesian tracking, where the probability of the state at time k is recursively computed from the probability of the state at time k-1 and from the measurement at time k. The Kalman filter is presented as an instance of Bayesian tracking for a non-stationary linear state transition model and Gaussian state and measurement processes. The general case of non-linear and non-Gaussian model can be difficult to deal with. To get good results, the approach to be adopted should fit the specific state transition and measurement model at hand. As examples, the talk will present the non-Gaussian parametric approach, the state-space discretization approach, and the sequential importance sampling approach based on particle filters.

Application of Bayesian tracking to the computation of mutual information between the state and the observation, and, in the case of Markov channels, between the input and the output of the channel, is discussed in the talk. Numerical results are presented for the channel affected by AWGN and multiplicative phase noise with memory.

Authors: Luca Barletta, Maurizio Magarini, and Arnaldo Spalvieri.

Biography:

Arnaldo Spalvieri, born in 1961, received the Laurea degree in Electronic Engineering in 1985. Formerly with Telettra S.p.A. (now Alcatel R.T.S), he has been an Assistant Professor since 1992, and an Associate Professor since 1998. His current interests include coded modulations and digital signal processing for Telecommunications