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In this paper polar codes are proposed for two receiver broadcast channelswith receiver message side information (BCSI) and noncausal state available atthe encoder, referred to as BCSI with noncausal state for short, where the tworeceivers know a priori the private messages intended for each other. Thischannel generalizes BCSI with common message and Gelfand-Pinsker problem andhas applications in cellular communication systems. We establish an achievablerate region for BCSI with noncausal state and show that it is strictly largerthan the straightforward extension of the Gelfand-Pinsker result. To achievethe established rate region with polar coding, we present polar codes for thegeneral Gelfand-Pinsker problem, which adopts chaining construction andutilizes causal information to pre-transmit the frozen bits. It is also shownthat causal information is necessary to pre-transmit the frozen bits. Based onthe result of Gelfand-Pinsker problem, we use the chaining construction methodto design polar codes for BCSI with noncausal state. The difficulty is thatthere are multiple chains sharing common information bit indices. To avoidvalue assignment conflicts, a nontrivial polarization alignment scheme ispresented. It is shown that the proposed rate region is tight for degraded BCSIwith noncausal state.

Polar Codes for Broadcast Channels with Receiver Message Side Information and Noncausal State Available at the Encoder