A note on the rate off decay off mean-square error with SNR for the AWGN channel

We consider a Gaussian source S with K samples that has to be transmitted over T = bK uses of an additive white Gaussian noise (AWGN) channel with signal-to-noise ratio (SNR) p. The distortion measure of interest, D(), is mean-square error (MSE). We consider the case when the SNR is not known at the transmitter. We are interested in characterizing the rate of decay of D() with in the high SNR limit, i.e., a(b) = limlog D()/log An upper bound, a(b) < 6, is obtained by considering the case when the SNR is known at the transmitter. Here, we propose a superposition scheme that can achieve an exponent a(b) arbitrarily close to b. This therefore characterizes the optimal distortion SNR exponent of the AWGN channel. Similar results were presented by Santhi and Vardy [1] for a uniform source for integer values of b. The scheme presented here extends the results of [1] to the Gaussian source and is applicable even for non integer values of b. We then consider an AWGN broadcast channel with two users having an SNR of 1 and 2 with 1 > 2 where the distortion for the weaker user is required to satisfy D(2) Dmin(2) for a constant > 1 where Dmin(2) is the minimum possible distortion achievable at SNR p2. We prove that we can obtain a decay rate of 1/1^b for the distortion of the stronger user for any > 1.

A note on the rate off decay off mean-square error with SNR for the AWGN channel Conference Paper