Zvi Reznic

Distortion Bounds for Broadcasting With Bandwidth Expansion

We consider the problem of broadcasting a single Gaussian source to two listeners over a Gaussian broadcast channel, with rho channel uses per source sample, where rho>1. A distortion pair (D1 ,D2) is said to be achievable if one can simultaneously achieve a mean-squared error (MSE) D1 at receiver 1 and D2 at receiver 2. The main result of this correspondence is an outer bound for the set of all achievable distortion pairs. That is, we find necessary conditions under which (D1,D2) is achievable. We then apply this result to the problem of point-to-point transmission over a Gaussian channel with unknown signal-to-noise ratio (SNR) and rho>1. We show that if a system must be optimal at a certain SNRmin, then, asymptotically, the system distortion cannot decay faster than O(1/SNR). As for achievability, we show that a previously reported scheme, due to Mittal and Phamdo (2002), is optimal at high SNR. We introduce two new schemes for broadcasting with bandwidth expansion, combining digital and analog transmissions. We finally show how a system with a partial feedback, returning from the bad receiver to the transmitter and to the good receiver, achieves a distortion pair that lies on the outer bound derived here

Distortion bounds for broadcasting with bandwidth expansion

We consider the problem of transmitting a Gaussian source over a Gaussian broadcast channel with p>1 channel uses per source sample. Our goal is to minimize simultaneously the squared-error distortion D/sub 1/ at receiver 1 (connected to the good channel) and D/sub 2/ at receiver 2 (connected to the bad channel). The distortion region, defined as the set of all simultaneously-achievable distortion pairs (D/sub 1/, D/sub 2/), is yet unknown. A separation-based system, consisting of a successive refinement source encoder followed by a broadcast channel encoder, is suboptimal. A variant of the problem is that of sending a Gaussian source over an AWGN channel, where the SNR is unknown except that SNR>SNR/sub min/ where SNR/sub min/ is known. In these conditions, the distortion cannot decay faster than 1/(SNR) as the SNR improves.

On the transmission of analog sources over channels with unknown SNR

We show that for every analog source with smooth density transmitted over an AWGN channel with unknown but high SNR, with one channel use per source sample, a single system achieves R(D) /spl ap/ C for all SNR. We also extend the results to non-Gaussian channel noise.