162 research outputs found
The Ergodic Capacity of Phase-Fading Interference Networks
We identify the role of equal strength interference links as bottlenecks on
the ergodic sum capacity of a user phase-fading interference network, i.e.,
an interference network where the fading process is restricted primarily to
independent and uniform phase variations while the channel magnitudes are held
fixed across time. It is shown that even though there are cross-links,
only about disjoint and equal strength interference links suffice to
determine the capacity of the network regardless of the strengths of the rest
of the cross channels. This scenario is called a \emph{minimal bottleneck
state}. It is shown that ergodic interference alignment is capacity optimal for
a network in a minimal bottleneck state. The results are applied to large
networks. It is shown that large networks are close to bottleneck states with a
high probability, so that ergodic interference alignment is close to optimal
for large networks. Limitations of the notion of bottleneck states are also
highlighted for channels where both the phase and the magnitudes vary with
time. It is shown through an example that for these channels, joint coding
across different bottleneck states makes it possible to circumvent the capacity
bottlenecks.Comment: 19 page
Elements of Cellular Blind Interference Alignment --- Aligned Frequency Reuse, Wireless Index Coding and Interference Diversity
We explore degrees of freedom (DoF) characterizations of partially connected
wireless networks, especially cellular networks, with no channel state
information at the transmitters. Specifically, we introduce three fundamental
elements --- aligned frequency reuse, wireless index coding and interference
diversity --- through a series of examples, focusing first on infinite regular
arrays, then on finite clusters with arbitrary connectivity and message sets,
and finally on heterogeneous settings with asymmetric multiple antenna
configurations. Aligned frequency reuse refers to the optimality of orthogonal
resource allocations in many cases, but according to unconventional reuse
patterns that are guided by interference alignment principles. Wireless index
coding highlights both the intimate connection between the index coding problem
and cellular blind interference alignment, as well as the added complexity
inherent to wireless settings. Interference diversity refers to the observation
that in a wireless network each receiver experiences a different set of
interferers, and depending on the actions of its own set of interferers, the
interference-free signal space at each receiver fluctuates differently from
other receivers, creating opportunities for robust applications of blind
interference alignment principles
Optimal Use of Current and Outdated Channel State Information - Degrees of Freedom of the MISO BC with Mixed CSIT
We consider a multiple-input-single-output (MISO) broadcast channel with
mixed channel state information at the transmitter (CSIT) that consists of
imperfect current CSIT and perfect outdated CSIT. Recent work by Kobayashi et
al. presented a scheme which exploits both imperfect current CSIT and perfect
outdated CSIT and achieves higher degrees of freedom (DoF) than possible with
only imperfect current CSIT or only outdated CSIT individually. In this work,
we further improve the achievable DoF in this setting by incorporating
additional private messages, and provide a tight information theoretic DoF
outer bound, thereby identifying the DoF optimal use of mixed CSIT. The new
result is stronger even in the original setting of only delayed CSIT, because
it allows us to remove the restricting assumption of statistically equivalent
fading for all users
Optimality of Orthogonal Access for One-dimensional Convex Cellular Networks
It is shown that a greedy orthogonal access scheme achieves the sum degrees
of freedom of all one-dimensional (all nodes placed along a straight line)
convex cellular networks (where cells are convex regions) when no channel
knowledge is available at the transmitters except the knowledge of the network
topology. In general, optimality of orthogonal access holds neither for
two-dimensional convex cellular networks nor for one-dimensional non-convex
cellular networks, thus revealing a fundamental limitation that exists only
when both one-dimensional and convex properties are simultaneously enforced, as
is common in canonical information theoretic models for studying cellular
networks. The result also establishes the capacity of the corresponding class
of index coding problems
The Capacity of Private Computation
We introduce the problem of private computation, comprised of distributed
and non-colluding servers, independent datasets, and a user who wants to
compute a function of the datasets privately, i.e., without revealing which
function he wants to compute, to any individual server. This private
computation problem is a strict generalization of the private information
retrieval (PIR) problem, obtained by expanding the PIR message set (which
consists of only independent messages) to also include functions of those
messages. The capacity of private computation, , is defined as the maximum
number of bits of the desired function that can be retrieved per bit of total
download from all servers. We characterize the capacity of private computation,
for servers and independent datasets that are replicated at each
server, when the functions to be computed are arbitrary linear combinations of
the datasets. Surprisingly, the capacity,
, matches the capacity of PIR with
servers and messages. Thus, allowing arbitrary linear computations does
not reduce the communication rate compared to pure dataset retrieval. The same
insight is shown to hold even for arbitrary non-linear computations when the
number of datasets
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