Tradeoff between source and channel coding

A problem in the transmission of analog information across a noisy discrete channel is the choice of channel code rate that optimally allocates the available transmission rate between lossy source coding and block channel coding. We establish tight bounds on the channel code rate that minimizes the average distortion of a vector quantizer cascaded with a channel coder and a binary symmetric channel. Analytic expressions are derived in the cases when the bit error probability is small and, also, when the source vector dimension is large. The optimal channel code rate is often substantially smaller than the channel capacity, and we obtain a noisy-channel version of the Zador high-resolution distortion formula