Distortion bounds for broadcasting with bandwidth expansion

Zvi Reznic*, Meir Feder, Ram Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the problem of broadcasting a single Gaussian source to two listeners over a Gaussian broadcast channel, with ρ channel uses per source sample, where ρ > 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 ρ > 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.

Original languageEnglish
Pages (from-to)3778-3788
Number of pages11
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2006


  • Distortion region
  • Joint source-channel coding
  • Lossy broadcasting


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