Remote coding of correlated sources with high resolution

In order to gain some insight into the results of direct coding and remote coding, the total rate loss caused by the separation of the encoders in the high resolution limit are studied. In the direct coding case, this loss is zero, since the rate in jointly encoding X and Y is given asymptotically, which coincides with the minimal rate sum of the separate encoders. In the remote coding case, however, the loss may be positive. This loss is due to the fact that at high resolution the quantization errors made by the separate encodings of X and Y are effectively uncorrelated. When the number of the remote sources is smaller than the number of measurements, the quantity equals infinity.