Two-user degraded broadcast channel with channel state information at transmitter and message side information at receivers

This paper investigates the two-user degraded broadcast channel with states where the channel state information is known at transmitter non-causally and the receivers know the message intended to the other as message side information. We characterize the capacity region by introducing two auxiliary random variables which can be viewed as an extension of Gel'fan and Pinsker coding. For the Gaussian case, we further show that within Gaussian input distributions the achievable rate region can be expressed using only one auxiliary random variable. We also provide the capacity region for two-user broadcast channel with non-causal state information at transmitter and message side information at weak receiver only.