On the Gaarder-Slepian “tracking system” conjecture [source coding]

The authors examine under what conditions, and with what notion of optimality, the coder of an optimal system can be operated with the information which is also accessible to the decoder. After a discussion of the difficulties involved, a theorem is proved for Markov sources which states that the extra memory of the coder can be substituted with independent randomization. The result is not tied to any specific notion of optimality. The main result is shown to hold for Markov sources of order k under weak assumptions on the structure and with respect to any per-letter fidelity criterion