  In this paper, a class of broadcast interference channels (BIC) is
investigated, where one of the two broadcast receivers is subject to
interference coming from a point-to-point transmission. For a general discrete
memoryless broadcast interference channel (DM-BIC), an achievable scheme based
on message splitting, superposition and binning is proposed and a concise
representation of the corresponding achievable rate region R is obtained. Two
partial-order broadcast conditions interference-oblivious less noisy and
interference-cognizant less noisy are defined, thereby extending the usual less
noisy condition for a regular broadcast channel by taking interference into
account. Under these conditions, a reduced form of R is shown to be equivalent
to a rate region based on a simpler scheme, where the broadcast transmitter
uses only superposition. Furthermore, if interference is strong for the
interference-oblivious less noisy DM-BIC, the capacity region is given by the
aforementioned two equivalent rate regions. For a Gaussian broadcast
interference channel (GBIC), channel parameters are categorized into three
regimes. For the first two regimes, which are closely related to the two
partial-order broadcast conditions, achievable rate regions are derived by
specializing the corresponding achievable schemes of DM-BICs with Gaussian
input distributions. The entropy power inequality (EPI) based outer bounds are
obtained by combining bounding techniques for a Gaussian broadcast channel
(GBC) and a Gaussian interference channel (GIC). These inner and outer bounds
lead to either exact or approximate characterizations of capacity regions and
sum capacity under various conditions. For the remaining complementing regime,
inner and outer bounds are also provided.
