Source coding with side information and a converse for degraded broadcast channels

Let{(X_i, Y_i,)}_{i=1}^{infty}be a memoryless correlated source with finite alphabets, and let us imagine that one person, encoder 1, observes onlyX^n = X_1,cdots,X_nand another person, encoder 2, observes onlyY^n = Y_1,cdots,Y_n. The encoders can produce encoding functionsf_n(X^n)andg_n(Y^n)respectively, which are made available to the decoder. We determine the rate region in case the decoder is interested only in knowingY^n = Y_1,cdots,Y_n(with small error probability). In Section H of the paper we give a characterization of the capacity region for degraded broadcast channels (DBC's), which was conjectured by Bergmans [11] and is somewhat sharper than the one obtained by Gallager [12].