14,611 research outputs found
Opportunistic Interference Mitigation Achieves Optimal Degrees-of-Freedom in Wireless Multi-cell Uplink Networks
We introduce an opportunistic interference mitigation (OIM) protocol, where a
user scheduling strategy is utilized in -cell uplink networks with
time-invariant channel coefficients and base stations (BSs) having
antennas. Each BS opportunistically selects a set of users who generate the
minimum interference to the other BSs. Two OIM protocols are shown according to
the number of simultaneously transmitting users per cell: opportunistic
interference nulling (OIN) and opportunistic interference alignment (OIA).
Then, their performance is analyzed in terms of degrees-of-freedom (DoFs). As
our main result, it is shown that DoFs are achievable under the OIN
protocol with selected users per cell, if the total number of users in
a cell scales at least as . Similarly, it turns out that
the OIA scheme with () selected users achieves DoFs, if scales
faster than . These results indicate that there exists a
trade-off between the achievable DoFs and the minimum required . By deriving
the corresponding upper bound on the DoFs, it is shown that the OIN scheme is
DoF optimal. Finally, numerical evaluation, a two-step scheduling method, and
the extension to multi-carrier scenarios are shown.Comment: 18 pages, 3 figures, Submitted to IEEE Transactions on Communication
On a zero speed sensitive cellular automaton
Using an unusual, yet natural invariant measure we show that there exists a
sensitive cellular automaton whose perturbations propagate at asymptotically
null speed for almost all configurations. More specifically, we prove that
Lyapunov Exponents measuring pointwise or average linear speeds of the faster
perturbations are equal to zero. We show that this implies the nullity of the
measurable entropy. The measure m we consider gives the m-expansiveness
property to the automaton. It is constructed with respect to a factor dynamical
system based on simple "counter dynamics". As a counterpart, we prove that in
the case of positively expansive automata, the perturbations move at positive
linear speed over all the configurations
Real Interference Alignment: Exploiting the Potential of Single Antenna Systems
In this paper, the available spatial Degrees-Of-Freedoms (DOF) in single
antenna systems is exploited. A new coding scheme is proposed in which several
data streams having fractional multiplexing gains are sent by transmitters and
interfering streams are aligned at receivers. Viewed as a field over rational
numbers, a received signal has infinite fractional DOFs, allowing simultaneous
interference alignment of any finite number of signals at any finite number of
receivers. The coding scheme is backed up by a recent result in the field of
Diophantine approximation, which states that the convergence part of the
Khintchine-Groshev theorem holds for points on non-degenerate manifolds. The
proposed coding scheme is proved to be optimal for three communication
channels, namely the Gaussian Interference Channel (GIC), the uplink channel in
cellular systems, and the channel. It is proved that the total DOF of the
-user GIC is almost surely, i.e. each user enjoys half of its
maximum DOF. Having cells and users within each cell in a cellular
system, the total DOF of the uplink channel is proved to be .
Finally, the total DOF of the channel with transmitters and
receivers is shown to be .Comment: Submitted to IEEE Transaction on Information Theory. The first
version was uploaded on arxiv on 17 Aug 2009 with the following title:
Forming Pseudo-MIMO by Embedding Infinite Rational Dimensions Along a Single
Real Line: Removing Barriers in Achieving the DOFs of Single Antenna System
Entropy rate of higher-dimensional cellular automata
We introduce the entropy rate of multidimensional cellular automata. This
number is invariant under shift-commuting isomorphisms; as opposed to the
entropy of such CA, it is always finite. The invariance property and the
finiteness of the entropy rate result from basic results about the entropy of
partitions of multidimensional cellular automata. We prove several results that
show that entropy rate of 2-dimensional automata preserve similar properties of
the entropy of one dimensional cellular automata.
In particular we establish an inequality which involves the entropy rate, the
radius of the cellular automaton and the entropy of the d-dimensional shift. We
also compute the entropy rate of permutative bi-dimensional cellular automata
and show that the finite value of the entropy rate (like the standard entropy
of for one-dimensional CA) depends on the number of permutative sites.
Finally we define the topological entropy rate and prove that it is an
invariant for topological shift-commuting conjugacy and establish some
relations between topological and measure-theoretic entropy rates
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
Is there a physically universal cellular automaton or Hamiltonian?
It is known that both quantum and classical cellular automata (CA) exist that
are computationally universal in the sense that they can simulate, after
appropriate initialization, any quantum or classical computation, respectively.
Here we introduce a different notion of universality: a CA is called physically
universal if every transformation on any finite region can be (approximately)
implemented by the autonomous time evolution of the system after the complement
of the region has been initialized in an appropriate way. We pose the question
of whether physically universal CAs exist. Such CAs would provide a model of
the world where the boundary between a physical system and its controller can
be consistently shifted, in analogy to the Heisenberg cut for the quantum
measurement problem. We propose to study the thermodynamic cost of computation
and control within such a model because implementing a cyclic process on a
microsystem may require a non-cyclic process for its controller, whereas
implementing a cyclic process on system and controller may require the
implementation of a non-cyclic process on a "meta"-controller, and so on.
Physically universal CAs avoid this infinite hierarchy of controllers and the
cost of implementing cycles on a subsystem can be described by mixing
properties of the CA dynamics. We define a physical prior on the CA
configurations by applying the dynamics to an initial state where half of the
CA is in the maximum entropy state and half of it is in the all-zero state
(thus reflecting the fact that life requires non-equilibrium states like the
boundary between a hold and a cold reservoir). As opposed to Solomonoff's
prior, our prior does not only account for the Kolmogorov complexity but also
for the cost of isolating the system during the state preparation if the
preparation process is not robust.Comment: 27 pages, 1 figur
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