Linear Analog Coding of Correlated Multivariate Gaussian Sources

The effect of prior knowledge when linear analog codes are used as joint source-channel codes for sources modeled as multivariate Gaussian processes is analyzed. We use information theoretic tools to evaluate the achievable performance gain obtained by exploiting prior knowledge. In order to assess the validity of linear codes in practical scenarios, where exact source statistics are not known, we study the effect of having partial knowledge of the statistics. We model the mismatch of the statistics as an additive perturbation matrix between the real covariance matrix and the postulated covariance matrix in the recovery process. In this setting, we obtain closed form expressions for a deterministic perturbation matrix and using random matrix theory tools we characterize the performance loss for i.i.d. random matrices.