The concept of stochastic complexity developed by Rissanen(1989) leads to consistent probability density estimators. These density estimators are defined to achieve the best compromise between likelihood and simplicity, namely, the stochastic complexity based on the observed sample. In this paper, a density estimation-based complexity decision rule is proposed which uses the quality of these estimators to estimate the corresponding unknown element of the true probability density. In the development, we introduce a loss function which includes the total variation of the squared distance of the characteristic functions to evaluate the performance of the density decision rule. The resulting complexity density decision procedure is shown to be admissible, to achieve the minimum expected risk, and to form a minimal complete class.>

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.>