  We consider the two-receiver memoryless broadcast channel with states where
each receiver requests both common and private messages, and may know part of
the private message requested by the other receiver as receiver message side
information (RMSI). We address two categories of the channel (i) channel with
states known causally to the transmitter, and (ii) channel with states known
non-causally to the transmitter. Starting with the channel without RMSI, we
first propose a transmission scheme and derive an inner bound for the causal
category. We then unify our inner bound for the causal category and the
best-known inner bound for the non-causal category, although their transmission
schemes are different. Moving on to the channel with RMSI, we first apply a
pre-coding to the transmission schemes of the causal and non-causal categories
without RMSI. We then derive a unified inner bound as a result of having a
unified inner bound when there is no RMSI, and applying the same pre-coding to
both categories. We show that our inner bound is tight for some new cases as
well as the cases whose capacity region was known previously.
