  We propose to send a Gaussian source over an average-power limited additive
white Gaussian noise channel by transmitting a linear combination of the source
sequence and the result of its quantization using a high dimensional Gaussian
vector quantizer. We show that, irrespective of the rate of the vector
quantizer (assumed to be fixed and smaller than the channel's capacity), this
transmission scheme is asymptotically optimal (as the quantizer's dimension
tends to infinity) under the mean squared-error fidelity criterion. This
generalizes the classical result of Goblick about the optimality of scaled
uncoded transmission, which corresponds to choosing the rate of the vector
quantizer as zero, and the classical source-channel separation approach, which
corresponds to choosing the rate of the vector quantizer arbitrarily close to
the capacity of the channel.
