77,410 research outputs found
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms
Mathematical programming is a branch of applied mathematics and has recently
been used to derive new decoding approaches, challenging established but often
heuristic algorithms based on iterative message passing. Concepts from
mathematical programming used in the context of decoding include linear,
integer, and nonlinear programming, network flows, notions of duality as well
as matroid and polyhedral theory. This survey article reviews and categorizes
decoding methods based on mathematical programming approaches for binary linear
codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory.
Published July 201
Random Rectangular Graphs
A generalization of the random geometric graph (RGG) model is proposed by
considering a set of points uniformly and independently distributed on a
rectangle of unit area instead of on a unit square [0,1]^2. The topological
properties of the random rectangular graphs (RRGs) generated by this model are
then studied as a function of the rectangle sides lengths a and b=1/a, and the
radius r used to connect the nodes. When a=1 we recover the RGG, and when
a-->infinity the very elongated rectangle generated resembles a one-dimensional
RGG. We obtain here analytical expressions for the average degree, degree
distribution, connectivity, average path length and clustering coefficient for
RRG. These results provide evidence that show that most of these properties
depend on the connection radius and the side length of the rectangle, usually
in a monotonic way. The clustering coefficient, however, increases when the
square is transformed into a slightly elongated rectangle, and after this
maximum it decays with the increase of the elongation of the rectangle. We
support all our findings by computational simulations that show the goodness of
the theoretical models proposed for RRGs.Comment: 23 pages, 8 figure
- …