Polar codes for broadcast channels with receiver message side information and noncausal state available at the encoder

In this paper polar codes are proposed for two receiver broadcast channels with receiver message side information (BCSI) and noncausal state available at the encoder, referred to as BCSI with noncausal state for short, where the two receivers know a priori the private messages intended for each other. An achievable rate region for BCSI with noncausal state is established and shown to strictly contain the straightforward extension of the Gelfand-Pinsker result. To achieve the established rate region, we present polar codes for the general Gelfand-Pinsker problem, which adopts chaining construction and utilizes causal information to pre-transmit the frozen bits. It is also shown that causal information is necessary to pre-transmit the frozen bits. Based on the result of Gelfand-Pinsker problem, we then propose polar codes for BCSI with noncausal state. The difficulty is that there are multiple chains sharing common information bit indices. To avoid value assignment conflicts, a nontrivial polarization alignment scheme is presented. It is shown that the proposed region is tight for degraded BCSI with noncausal state.