  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. This
channel generalizes BCSI with common message and Gelfand-Pinsker problem and
has applications in cellular communication systems. We establish an achievable
rate region for BCSI with noncausal state and show that it is strictly larger
than the straightforward extension of the Gelfand-Pinsker result. To achieve
the established rate region with polar coding, 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 use the chaining construction method
to design 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 rate region is tight for degraded BCSI
with noncausal state.
