Superimposed Coded and Uncoded Transmissions of a Gaussian Source over the Gaussian Channel

Details Superimposed Coded and Uncoded Transmissions of a Gaussian Source over the Gaussian Channel Superimposed Coded and Uncoded Transmissions of a Gaussian Source over the Gaussian Channel

2006-01-09

arxiv.org/abs/cs/0601028v2

Computer Science

Information Theory

three pages, to appear in Proceedings International Symposium on Information Theory 2006

Scientific paper

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.

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