Information rates for Poisson sequences

The rate-distortion function of a Poisson sequence, under a single-letter magnitude-error distortion measure is derived and studied. Simple approximations to the rate-distortion curve for low and high distortions are obtained. A useful lower bound to this curve is derived and an upper bound is generated by a simple instrumentable coding scheme. The rate-distortion relationship for the latter is seen to be nearly ideal over a large distortion region.