A Note on the Rate of Decay of Mean-Squared Error With SNR for the AWGN Channel

The problem of transmitting a Gaussian source over an additive white Gaussian noise (AWGN) channel when the channel signal-to-noise ratio (SNR) is unknown at the transmitter and is known at the receiver is considered. The performance metric used is distortion SNR exponent which is defined as the rate of decay of mean-squared error (MSE) distortion with SNR. The optimal exponent is shown to be equal to the ratio of the number of channel uses to number of source samples. A superposition-based scheme is proposed that can achieve an exponent arbitrarily close to the optimal value.