An important class of universal encoders is the one where theencoder is fed with two inputs: a) the incoming string of data to becompressed, b) a “training sequence” that consists of thelast N data symbols that have been processed (i.e. a sliding windowalgorithm). We consider fixed-to-variable universal encoders thatnoiselessly compress blocks of some fixed length and derive universalbounds on the rate of approach of the compression to the l-th order (perletter) entropy H(X1l) or to the smallerconditional entropy H(X1l-k|X0-k+1) as a function of l and of the length N of the training sequenceX0-N+1展开▼