Optimal linear labelling for the minimization of both source and channel distortion

We present an approach for joint source-channel coding based on the minimisation of channel distortion and then source distortion. It has previously been proved that distortion due to a binary symmetric channel is minimized by a linear labelling. In this paper, we show how to obtain an asymptotically optimal linear labelling which also minimizes the source distortion for Gaussian sources. This linear labelling is based on the notion of component diversity which can be obtained by algebraic constructions derived from number theory.