Duality theorems for joint source-channel coding

Abstract

We consider joint source-channel coding for a memoryless Gaussian source and an additive white Gaussian noise (AWGN) channel. For a given code defined by an encoder-decoder pair (/spl alpha/, /spl beta/), its dual code is obtained by interchanging the encoder and decoder: (/spl beta/, /spl alpha/). It is shown that if a code (/spl alpha/, /spl beta/) is optimal at rate p channel uses per source sample and if it satisfies a certain uniform continuity condition, then its dual code (/spl beta/, /spl alpha/) is optimal for rate 1//spl rho/ channel uses per source sample. Further, it is demonstrated that there is a code which is optimal but its dual code is not optimal. Finally, using random coding, we show that there is an optimal code which has an optimal dual. The duality concept is also presented for the cases of (i) binary memoryless equiprobable source and binary-symmetric channel (BSC), and (ii) colored Gaussian source and additive colored Gaussian noise (ACGN) channel.