Approaching R(D) = C in colored joint source/channel broadcasting by prediction

We consider transmission of a colored Gaussian source through a power constrained colored Gaussian broadcast channel subject to a mean-squared error distortion measure. It is well known that separation of source and channel coding cannot achieve the point R(D) = C simultaneously for more than one receiver. We characterize the distortion region achieved by the recently proposed joint source/channel "analog matching" coding scheme. In the special case of equal bandwidth (but arbitrary source and channel spectra) and in the limit of high signal to noise ratio (SNR), we prove that full robustness is asymptotically possible, i.e., the encoder becomes SNR-independent and each decoder approaches the ideal performance R(D) = C. This result extends the well known optimality of analog transmission in the white source / white channel case. Our results are based upon an encoder which employs modulo-lattice arithmetics, i.e. the transmitted signal is the residue of an analog signal with respect to a lattice.