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

TL;DR

This paper introduces a transmission scheme combining coded and uncoded methods for Gaussian sources over Gaussian channels, proving its asymptotic optimality regardless of the quantizer rate, thus generalizing classical results.

Contribution

It presents a novel superimposed transmission scheme that remains optimal for Gaussian sources over Gaussian channels, extending classical uncoded and separation approaches.

Findings

The scheme is asymptotically optimal as quantizer dimension increases.

It generalizes Goblick's uncoded transmission optimality.

It bridges uncoded and separation strategies in source-channel coding.

Abstract

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.