In a wireless network with a single source and a single destination and an
arbitrary number of relay nodes, what is the maximum rate of information flow
achievable? We make progress on this long standing problem through a two-step
approach. First we propose a deterministic channel model which captures the key
wireless properties of signal strength, broadcast and superposition. We obtain
an exact characterization of the capacity of a network with nodes connected by
such deterministic channels.
We study the capacity of secret-key agreement over a wiretap channel with
state parameters. The transmitter communicates to the legitimate receiver and
the eavesdropper over a discrete memoryless wiretap channel with a memoryless
state sequence. The transmitter and the legitimate receiver generate a shared
secret key, that remains secret from the eavesdropper. No public discussion
channel is available. The state sequence is known noncausally to the
transmitter. We derive lower and upper bounds on the secret-key capacity.
Recently, it has been shown that a quantize-map-and-forward scheme
approximately achieves (within a constant number of bits) the Gaussian relay
network capacity for arbitrary topologies. This was established using Gaussian
codebooks for transmission and random mappings at the relays. In this paper, we
show that the same approximation result can be established by using lattices
for transmission and quantization along with structured mappings at the relays.
We consider the source-channel separation architecture for lossy source
coding in general communication networks. It is shown that the separation
approach is optimal in two general scenarios, and is approximately optimal in a
third scenario.
We consider the problem of multicasting information from a source to a set of
receivers over a network where intermediate network nodes perform randomized
network coding operations on the source packets. We propose a channel model for
the non-coherent network coding introduced by Koetter and Kschischang in [5],
that captures the essence of such a network operation, and calculate the
capacity as a function of network parameters.
Wireless network topologies change over time and maintaining routes requires
frequent updates. Updates are costly in terms of consuming throughput available
for data transmission, which is precious in wireless networks. In this paper,
we ask whether there exist low-overhead schemes that produce low-stretch
routes. This is studied by using the underlying geometric properties of the
connectivity graph in wireless networks.
This paper addresses the problem of finding the nearest neighbor (or one of
the R-nearest neighbors) of a query object q in a database of n objects. In
contrast with most existing approaches, we can only access the ``hidden'' space
in which the objects live through a similarity oracle. The oracle, given two
reference objects and a query object, returns the reference object closest to
the query object. The oracle attempts to model the behavior of human users,
capable of making statements about similarity, but not of assigning meaningful
numerical values to distances between objects.