Francois Baccelli INRIA ENS Information Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements Authors Venkat Anantharam Francois Baccelli

Abstracts – Francois Baccelli (INRIA ,ENS) Information-Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements Authors : Venkat Anantharam, Francois Baccelli Abstract : This paper studies the Shannon regime for the random displacement of stationary point processes. Let each point of some initial stationary point process in Rn give rise to one daughter point, the location of which is obtained by ad- ding a random vector to the coordinates of the mother point, with all displacement vectors independently and identically distributed for all points. The decoding problem is then the following one : the whole mother point process is known as well as the coordinates of some daughter point ; the displa- cements are only known through their law ; can one find the mother of this daughter point ? The Shannon regime is that where the dimension n tends to infinity and where the loga- rithm of the intensity of the point process is proportional to n. We show that this problem exhibits a sharp threshold : if the sum of the proportionality factor and of the differen- tial entropy rate of the noise is positive, then the probability of finding the right mother point tends to 0 with n for all point processes and decoding strategies. If this sum is nega- tive, there exist mother point processes, for instance Poisson, and decoding strategies, for instance maximum likelihood, for which the probability of finding the right mother tends to 1 with n.

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