Colored Gaussian Source-Channel Broadcast for Heterogeneous (Analog/Digital) Receivers

The problem of transmitting a Gaussian source with memory to a digital and a linear-analog receiver, over an arbitrarily colored, nondegraded Gaussian broadcast channel is studied. The main result of this work is a complete characterization of the set of achievable distortion pairs at the two receivers given a power constraint at the transmitter. Further, a constructive hybrid uncoded-coded scheme consisting of the cascade of source coding with side information and channel coding with side information systems is shown to achieve the entire power-mean squared error (MSE) distortion region associated with the problem. An interesting operating point in this region is one where the digital receiver obtains the classical point-to-point optimal quality and the analog receiver attains the best possible simultaneously achievable distortion. This problem is motivated by the practical application of the seamless ldquoin-bandrdquo digital upgrade of legacy analog transmission systems.