  We address single-user data transmission over a channel where the received
signal incurs interference from a finite number of users (interfering users)
that use single codebooks for transmitting their own messages. The receiver,
however, is allowed to decode interfering users' messages. This means the
signal transmitted from any interfering user is either decoded or considered as
noise at the receiver side. We propose the following method to obtain an
achievable rate for this channel. Assuming its own data is decoded
successfully, the receiver partitions the set of interfering users into two
disjoint subsets, namely the set of decodable users and the set of
non-decodable users. Then the transmitter's rate is chosen such that the
intended signal can be jointly decoded with the set of decodable users. To show
the strength of this method, we prove that for the additive Gaussian channel
with Gaussian interfering users, the Gaussian distribution is optimal and the
achievable rate is the capacity of this channel. To obtain the maximum
achievable rate, one needs to find the maximum decodable subset of interfering
users. Due to the large number of possible choices, having efficient algorithms
that find the set of decodable users with maximum cardinality is desired. To
this end, we propose an algorithm that enables the receiver to accomplish this
task in polynomial time.
