Tradeoff between source and channel coding on a Gaussian channel

Consider a system that quantizes and encodes analog data for transmission across an additive noise Gaussian channel. To minimize distortion, the channel code rate must be chosen to optimally allocate the available transmission rate between lossy source coding and block channel coding. We establish tight upper and lower bounds an the channel code rate that minimizes the average distortion of a vector quantizer cascaded with a channel coder and a Gaussian channel, thus extending some recently obtained results for the binary-symmetric channel. The upper bounds are obtained by averaging, whereas the lower bounds are uniform, over all possible index assignments. Analytic expressions are derived for large and small signal-to-noise ratios, and also for large source vector dimension. As in the binary-symmetric channel, the optimal channel code rate is often substantially smaller than the channel capacity and the distortion decays exponentially with the number of channel uses. Exact exponents are derived.