Some techniques in universal source coding and during for composite sources

We consider three problems in source coding. First, we consider the composite source model. A composite source has a switch driven by a random process which selects one of a possible set of subsources. We derive some convergence results for estimation of the switching process, and use these to prove that the entropy of some composite sources may be computed. some coding techniques for composite sources are also presented and their performance is bounded. Next, we construct a variable-length-to-fixed-length (VL-FL) universal code for a class of unifilar Markov sources. A VL-FL code maps strings of source outputs into fixed-length codewords. We show that the redundancy of the code converges to zero uniformly over the class of sources as the blocklength increases. The code is also universal with respect to the initial state of the source. We compare the performance of this code to FL-VL universal codes. We then consider universal coding for real-valued sources. We show that given some coding technique for a known source, we may construct a code for a class of sources. We show that this technique works for some classes of memoryless sources, and also for a compact subset of the class of k-th order Gaussian autoregressive sources.