Source identification and compression of mixture data from finite observations

We consider the problem of the identification of a mixture of ergodic stationary sources from a limited number of finite-length observations of a mixture. We propose an algorithm based on Bayesian Information Criterion and Expectation Maximization to identify the sources' models and estimate the mixture parameters. Based on this algorithm, the sources' distributions can be computed and used for nearly optimal memory-assisted coding of the sequences generated by the mixture. Further, we provide upper and lower bounds on the entropy of the mixture source and show that it converges to the upper bound as the length of the sequences increases and derive the convergence rate for the per-symbol entropy of the mixture of finite memory sources.