Toward a source coding theory for sets

The problem of communicating (unordered) sets, rather than (ordered) sequences is formulated. Elementary results in all major branches of source coding theory, including lossless coding, high-rate and low-rate quantization, and rate distortion theory are presented. In certain scenarios, rate savings of log n! bits for sets of size n are obtained. Asymptotically in the set size, the entropy rate is zero and for sources with an ordered parent alphabet, the (0,0) point is the rate distortion function.