37,332 research outputs found
High-SNR Capacity of Wireless Communication Channels in the Noncoherent Setting: A Primer
This paper, mostly tutorial in nature, deals with the problem of
characterizing the capacity of fading channels in the high signal-to-noise
ratio (SNR) regime. We focus on the practically relevant noncoherent setting,
where neither transmitter nor receiver know the channel realizations, but both
are aware of the channel law. We present, in an intuitive and accessible form,
two tools, first proposed by Lapidoth & Moser (2003), of fundamental importance
to high-SNR capacity analysis: the duality approach and the escape-to-infinity
property of capacity-achieving distributions. Furthermore, we apply these tools
to refine some of the results that appeared previously in the literature and to
simplify the corresponding proofs.Comment: To appear in Int. J. Electron. Commun. (AE\"U), Aug. 201
Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility
The revenue optimal mechanism for selling a single item to agents with
independent but non-identically distributed values is complex for agents with
linear utility (Myerson,1981) and has no closed-form characterization for
agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for
linear utility agents satisfying a natural regularity property, Alaei et al.
(2018) showed that simply posting an anonymous price is an e-approximation. We
give a parameterization of the regularity property that extends to agents with
non-linear utility and show that the approximation bound of anonymous pricing
for regular agents approximately extends to agents that satisfy this
approximate regularity property. We apply this approximation framework to prove
that anonymous pricing is a constant approximation to the revenue optimal
single-item auction for agents with public-budget utility, private-budget
utility, and (a special case of) risk-averse utility.Comment: Appeared at EC 201
Product Multicommodity Flow in Wireless Networks
We provide a tight approximate characterization of the -dimensional
product multicommodity flow (PMF) region for a wireless network of nodes.
Separate characterizations in terms of the spectral properties of appropriate
network graphs are obtained in both an information theoretic sense and for a
combinatorial interference model (e.g., Protocol model). These provide an inner
approximation to the dimensional capacity region. These results answer
the following questions which arise naturally from previous work: (a) What is
the significance of in the scaling laws for the Protocol
interference model obtained by Gupta and Kumar (2000)? (b) Can we obtain a
tight approximation to the "maximum supportable flow" for node distributions
more general than the geometric random distribution, traffic models other than
randomly chosen source-destination pairs, and under very general assumptions on
the channel fading model?
We first establish that the random source-destination model is essentially a
one-dimensional approximation to the capacity region, and a special case of
product multi-commodity flow. Building on previous results, for a combinatorial
interference model given by a network and a conflict graph, we relate the
product multicommodity flow to the spectral properties of the underlying graphs
resulting in computational upper and lower bounds. For the more interesting
random fading model with additive white Gaussian noise (AWGN), we show that the
scaling laws for PMF can again be tightly characterized by the spectral
properties of appropriately defined graphs. As an implication, we obtain
computationally efficient upper and lower bounds on the PMF for any wireless
network with a guaranteed approximation factor.Comment: Revised version of "Capacity-Delay Scaling in Arbitrary Wireless
Networks" submitted to the IEEE Transactions on Information Theory. Part of
this work appeared in the Allerton Conference on Communication, Control, and
Computing, Monticello, IL, 2005, and the Internation Symposium on Information
Theory (ISIT), 200
Second-order coding rates for pure-loss bosonic channels
A pure-loss bosonic channel is a simple model for communication over
free-space or fiber-optic links. More generally, phase-insensitive bosonic
channels model other kinds of noise, such as thermalizing or amplifying
processes. Recent work has established the classical capacity of all of these
channels, and furthermore, it is now known that a strong converse theorem holds
for the classical capacity of these channels under a particular photon number
constraint. The goal of the present paper is to initiate the study of
second-order coding rates for these channels, by beginning with the simplest
one, the pure-loss bosonic channel. In a second-order analysis of
communication, one fixes the tolerable error probability and seeks to
understand the back-off from capacity for a sufficiently large yet finite
number of channel uses. We find a lower bound on the maximum achievable code
size for the pure-loss bosonic channel, in terms of the known expression for
its capacity and a quantity called channel dispersion. We accomplish this by
proving a general "one-shot" coding theorem for channels with classical inputs
and pure-state quantum outputs which reside in a separable Hilbert space. The
theorem leads to an optimal second-order characterization when the channel
output is finite-dimensional, and it remains an open question to determine
whether the characterization is optimal for the pure-loss bosonic channel.Comment: 18 pages, 3 figures; v3: final version accepted for publication in
Quantum Information Processin
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