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

Abstract: 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.