Source and channel coding tradeoff 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 approximations of the channel code rate that minimizes the average distortion of a vector quantizer cascaded with a channel coder and a Gaussian channel, thus complementing some recently-obtained results for the binary symmetric channel. Analytic expressions are derived for large signal-to-noise ratios and for large source vector dimension. As in the binary symmetric channel, the distortion decays exponentially with the number of channel uses