The source coding theory of information theory is applied to the digital processing of synthetic aperture radar signals. A lower bound is established on the data rate that must exist at any point in the processing flow, in particular at the conversion from analog-to-digital (A/D) signals, to achieve a given output map signal-to-noise ratio. The usual linear uniform-step A/D conversion of in-phase and quadrature coherent video signals is found to provide a given output map signal-to-noise ratio with a data rate within about 20 percent of the derived lower bound.