Source coding for a noiseless broadcast channel with partial receiver side information

A transmitter communicates the outputs X, Y from a finite discrete memoryless source to two receivers via a noiseless broadcast channel. Each message is required at only one receiver, the receivers cannot cooperate, and one receiver has side information U. We show the achievable communication rates for this channel are R H(Y )+H(X|Y,U). Achievability is proved via a rate-split version of random binning. Cut-set outer bounds are not tight, so an alternate converse is presented. This problem is an example of a broadcast network, with m messages and m independent receivers each having different sideinformation. This broadcast network is motivated by a control information problem from mobile networking, and it generalizes the Wyner-Ziv, Heegard-Berger, and Sgarro problems.