A Note on the Broadcast Channel With Stale State Information at the Transmitter

This paper shows that the Maddah-Ali-Tse (MAT) scheme, which achieves the symmetric capacity of two example broadcast channels with strictly causal state information at the transmitter, is a simple special case of the Shayevitz-Wigger (SW) scheme for the broadcast channel with generalized feedback, which involves block Markov coding, Gray-Wyner compression, superposition coding, and Marton coding. Focusing on the class of symmetric broadcast channels with state, we derive an expression for the maximum achievable symmetric rate using the SW scheme. We show that the MAT results for the two-receiver case can be recovered by evaluating this expression for the special case in which superposition coding and Marton coding are not used. We then introduce a new broadcast channel example that shares many features of the MAT examples. We show that another special case of our maximum symmetric rate expression in which superposition coding is also used attains a higher symmetric rate than the MAT scheme. The symmetric capacity of this new example is not known, however.