For every individual infinite sequence u we define a distortion-rate function d (R| u) which is
shown to be an asymptotically attainable lower bound on the distortion that can be achieved
for u by any finite-state encoder which operates at a fixed output information rate R. This is
done by means of a coding theorem and its converse. No probabilistic characterization of u
is assumed. The coding theorem demonstrates the existence of {\em universal} encoders
which are asymptotically optimal for every infinite sequence over a given finite alphabet. The …