The capacity region of the parallel partially cooperative relay broadcast channel with unmatched degraded subchannels

We investigate the parallel partially cooperative relay broadcast channel with unmatched degraded subchannels. We characterize the capacity region of this channel in the general setting that, transmitter sends a common message for both users and a private message for each of them. Our achievability result is based on the choosing appropriate parameters for the general achievable rate region of partially cooperative relay broadcast channel. We provide a converse proof for this achievable region as well, which establishes the capacity region.