  An Interference Channel with Generalized Feedback (IFC-GF) is a model for a
wireless network where several source-destination pairs compete for the same
channel resources, and where the sources have the ability to sense the current
channel activity. The signal overheard from the channel provides information
about the activity of the other users, and thus furnishes the basis for
cooperation. In this two-part paper we study achievable strategies and outer
bounds for a general IFC-GF with two source-destination pairs. We then evaluate
the proposed regions for the Gaussian channel. Part I: achievable region. We
propose that the generalized feedback is used to gain knowledge about the
message sent by other user and then exploited in two ways: (a) to {\em relay}
the messages that can be decoded at both destinations--thus realizing the gains
of beam-forming of a distributed multi-antenna system--and (b) to {\em hide}
the messages that can not be decoded at the non-intended destination--thus
leveraging the interference "pre-cancellation" property of dirty-paper-type
coding. We show that our achievable region generalizes several known achievable
regions for IFC-GF and that it reduces to known achievable regions for some of
the channels subsumed by the IFC-GF model.
