Two-dimensional encoding by finite-state encoders

Distortion-free compressibility of individual pictures by finite-state encoders is investigated. In a recent paper (see IEEE Trans. Inform. Theory, vol.32, no.1, p.1-8, 1986) the compressibility of a given picture I was defined and shown to be the asymptotically attainable lower bound on the compression ratio that can be achieved for I by any finite-state encoder. Here, a different and more direct approach is taken to prove similar results, which are summarized in a converse-to-coding theorem and a constructive-coding-theorem that leads to a universal asymptotically optimal compression algorithm