Laplacian channel state estimation for state dependent channels

In this paper, we extend the results for optimal transmission of the Gaussian channel state via the state-dependent channels to the communications of the Laplacian data. We derive a minimum mean square estimate (MMSE) of the stationary independent identically (i.i.d.) distributed Laplacian channel state corrupted by an additive white Gaussian noise (AWGN) and demonstrate that estimation accuracy is the same in both cases and does not depend on the channel state pdf. For transmission performance improvement we propose to decompose the Laplacian data using the paradygm of parallel source splitting. We show that for the case of infinite Gaussian mixture approximation of Laplacian source it is possible to significantly improve the performance of the considered communication protocol.