On the Asymptotic Distortion Behavior of the Distributed Karhunen-Loève Transform

The ability to design efficient distributed communications systems heavily depends on a proper understanding of the distortion incurred by their constituting elements. To this end, we study the mean squared reconstruction error behavior of the distributed Karhunen-Lo`{e}ve transform. We provide a general formula to compute this distortion under asymptotic considerations in a pure approximation viewpoint. Using a simple illustrative example, we show how this approach allows to obtain closed-form formulas that permit to efficiently assess the performance of the distributed scheme.