Duality between Broadcasting with Bandwidth Expansion and Bandwidth Compression

We consider the problem of broadcasting kldr samples of an independent identically distributed (i.i.d) Gaussian source to two users in n = lambdakldr uses of an AWGN channel. We develop a framework which shows a duality between a source-channel coding scheme for the case of lambda > 1 and that for lambda < 1. Using this duality, we derive a scheme for the case of lambda < 1, which is the dual of a scheme proposed by Reznic, Zamir and Feder (2006). This scheme, which provides the largest known achievable distortion region currently known, is also the same as that proposed by Prabhakaran et al (2005) specialized to the case of an i.i.d source with lambda < 1. We also provide an explanation for why this scheme performs well by first analyzing the performance of source-channel coding schemes in the presence of a signal-to- noise ratio mismatch.