23,614 research outputs found
Compute-and-Forward Can Buy Secrecy Cheap
We consider a Gaussian multiple access channel with transmitters, a
(intended) receiver and an external eavesdropper. The transmitters wish to
reliably communicate with the receiver while concealing their messages from the
eavesdropper. This scenario has been investigated in prior works using two
different coding techniques; the random i.i.d. Gaussian coding and the signal
alignment coding. Although, the latter offers promising results in a very high
SNR regime, extending these results to the finite SNR regime is a challenging
task. In this paper, we propose a new lattice alignment scheme based on the
compute-and-forward framework which works at any finite SNR. We show that our
achievable secure sum rate scales with and hence, in most
SNR regimes, our scheme outperforms the random coding scheme in which the
secure sum rate does not grow with power. Furthermore, we show that our result
matches the prior work in the infinite SNR regime. Additionally, we analyze our
result numerically.Comment: Accepted to ISIT 2015, 5 pages, 3 figure
Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records
In these lecture notes I will discuss the universal first-passage properties
of a simple correlated discrete-time sequence {x_0=0, x_1,x_2.... x_n} up to n
steps where x_i represents the position at step i of a random walker hopping on
a continuous line by drawing independently, at each time step, a random jump
length from an arbitrary symmetric and continuous distribution (it includes,
e.g., the Levy flights). I will focus on the statistics of two extreme
observables associated with the sequence: (i) its global maximum and the time
step at which the maximum occurs and (ii) the number of records in the sequence
and their ages. I will demonstrate how the universal statistics of these
observables emerge as a consequence of Pollaczek-Spitzer formula and the
associated Sparre Andersen theorem.Comment: Lecture notes for the summer school "Fundamental Problems in
Statistical Physics: XII" held at Leuven, Belgium (2009). 20 pages, 4
figures; typos corrected, a figure redrawn and new references and discussions
adde
Branching Instabilities in Rapid Fracture: Dynamics and Geometry
We propose a theoretical model for branching instabilities in 2-dimensional
fracture, offering predictions for when crack branching occurs, how multiple
cracks develop, and what is the geometry of multiple branches. The model is
based on equations of motion for crack tips which depend only on the time
dependent stress intensity factors. The latter are obtained by invoking an
approximate relation between static and dynamic stress intensity factors,
together with an essentially exact calculation of the static ones. The results
of this model are in good agreement with a sizeable quantity of experimental
data.Comment: 9 pages, 11 figure
Integer-Forcing Source Coding
Integer-Forcing (IF) is a new framework, based on compute-and-forward, for
decoding multiple integer linear combinations from the output of a Gaussian
multiple-input multiple-output channel. This work applies the IF approach to
arrive at a new low-complexity scheme, IF source coding, for distributed lossy
compression of correlated Gaussian sources under a minimum mean squared error
distortion measure. All encoders use the same nested lattice codebook. Each
encoder quantizes its observation using the fine lattice as a quantizer and
reduces the result modulo the coarse lattice, which plays the role of binning.
Rather than directly recovering the individual quantized signals, the decoder
first recovers a full-rank set of judiciously chosen integer linear
combinations of the quantized signals, and then inverts it. In general, the
linear combinations have smaller average powers than the original signals. This
allows to increase the density of the coarse lattice, which in turn translates
to smaller compression rates. We also propose and analyze a one-shot version of
IF source coding, that is simple enough to potentially lead to a new design
principle for analog-to-digital converters that can exploit spatial
correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor
Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow
Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, non-linear magnetohydrodynamic process whose study is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows
Compute-and-Forward: Harnessing Interference through Structured Codes
Interference is usually viewed as an obstacle to communication in wireless
networks. This paper proposes a new strategy, compute-and-forward, that
exploits interference to obtain significantly higher rates between users in a
network. The key idea is that relays should decode linear functions of
transmitted messages according to their observed channel coefficients rather
than ignoring the interference as noise. After decoding these linear equations,
the relays simply send them towards the destinations, which given enough
equations, can recover their desired messages. The underlying codes are based
on nested lattices whose algebraic structure ensures that integer combinations
of codewords can be decoded reliably. Encoders map messages from a finite field
to a lattice and decoders recover equations of lattice points which are then
mapped back to equations over the finite field. This scheme is applicable even
if the transmitters lack channel state information.Comment: IEEE Trans. Info Theory, to appear. 23 pages, 13 figure
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