  In this paper we study the reception zones of a wireless network in the SINR
model with receivers that employ \emph{interference cancellation} (IC), a
technique that allows a receiver to decode interfering signals, and
\emph{cancel} them from the received signal in order to decode its intended
message. We first derive some important topological properties of the diagram
describing the reception zones and their connections to \emph{high-order
Voronoi diagrams} and other related geometric objects. We then discuss the
computational issues that arise when seeking an efficient description of the
zones. Our main fundamental result states that although potentially there are
exponentially many possible cancellation orderings (and consequently reception
cells), in fact there are much fewer nonempty such cells. We prove a (tight)
linear bound on the number of cells and provide a polynomial time algorithm to
describe the diagram. Moreover, we introduce a novel measure, referred to as
the \emph{Compactness Parameter}, which influences the tightness of our bounds.
We then utilize the properties established for reception diagrams to devise a
logarithmic time algorithm for answering \emph{point-location} queries for
networks with IC.
