K Gautam Shenoy, Vinod Sharma
Comments: 18 pages, 1 Figure
Subjects: Information Theory (cs.IT)
We study DMC and AWGN channels when the transmitter harvests energy from the
environment. These can model wireless sensor networks as well as Internet of
Things. We study such channels with infinite energy buffer in the finite
blocklength regime and provide the corresponding achievability and converse
results.
Peter Larsson, Lars K. Rasmussen, Mikael Skoglund
Subjects: Information Theory (cs.IT)
In [1], we introduced a new, matrix algebraic, performance analysis framework
for wireless systems with fading channels based on the matrix exponential
distribution. The main idea was to use the compact, powerful, and easy-to-use,
matrix exponential (ME)-distribution for i) modeling the unprocessed channel
signal to noise ratio (SNR), ii) exploiting the closure property of the
ME-distribution for SNR processing operations to give the effective channel
random variable (r.v.) on ME-distribution form, and then to iii) express the
performance measure in a closed-form based on ME-distribution matrix/vector
parameters only. In this work, we aim to more clearly present, formalize,
refine and develop this unified bottom-up analysis framework, show its
versatility to handle important communication cases, performance evaluation
levels, and performance metrics. The bivariate ME-distribution is introduced
here as yet another useful ME-tool, e.g. to account for dependency among two
r.v.s. We propose that the ME-distribution may, in addition to fading, also
characterize the pdf of discrete-time signal r.v.s, thus extending the
ME-distribution matrix form to new generalized 1D/2D-Gaussian-, and Rayleigh-,
distribution-like matrix forms. Our findings here, strengthen the observation
from [1], [2], and indicates that the ME-distribution can be a promising tool
for wireless system modeling and performance analysis.
Yongbo Xia, Nian Li, Xiangyong Zeng, Tor Helleseth
Subjects: Information Theory (cs.IT)
In this paper, let (n=2m) and (d=3^{m+1}-2) with (mgeq2) and
(gcd(d,3^n-1)=1). By studying the weight distribution of the ternary
Zetterberg code and counting the numbers of solutions of some equations over
the finite field (mathbb{F}_{3^n}), the correlation distribution between a
ternary (m)-sequence of period (3^n-1) and its (d)-decimation sequence is
completely determined. This is the first time that the correlation distribution
for a non-binary Niho decimation has been determined since 1976.
Yulong Zou
Comments: 11 pages, 6 figures, IEEE Transactions on Wireless Communications, 2017
Subjects: Information Theory (cs.IT)
In this paper, we examine the physical-layer security for a spectrum sharing
system consisting of multiple source-destination pairs, which dynamically
access their shared spectrum for data transmissions in the presence of an
eavesdropper. We propose a source cooperation (SC) aided opportunistic jamming
framework for protecting the transmission confidentiality of the spectrum
sharing system against eavesdropping. Specifically, when a source node is
allowed to access the shared spectrum for data transmissions, another source is
opportunistically selected in the spectrum sharing system to transmit an
artificial noise for disrupting the eavesdropper without affecting the
legitimate transmissions. We present two specific SC aided opportunistic
jamming schemes, namely the SC aided random jammer selection (RJS) and optimal
jammer selection (OJS), which are referred to as the SC-RJS and SC-OJS,
respectively. We also consider the conventional non-cooperation as a baseline.
We derive closed-form intercept probability expressions for the
non-cooperation, SC-RJS and SC-OJS schemes, based on which their secrecy
diversity gains are determined through an asymptotic intercept probability
analysis in the high signal-to-noise ratio (SNR) region. It is proved that the
conventional non-cooperation exhibits a secrecy diversity of zero, whereas the
proposed SC-RJS and SC-OJS achieve a higher secrecy diversity of one. This also
surprisingly means that no additional secrecy diversity gain is achieved by the
optimal jammer selection compared to the random selection strategy. In
addition, numerical results show that the intercept probability performance of
the SC-OJS is always better than that of the SC-RJS and non-cooperation, even
when the legitimate channel is worse than the eavesdropping channel.
Jinsong Hu, Shihao Yan, Feng Shu, Jiangzhou Wang, Jun Li, Yijin Zhang
Subjects: Information Theory (cs.IT)
In this paper, we propose a novel directional modulation (DM) scheme based on
random frequency diverse arrays with artificial noise (RFDA-DM-AN) to enhance
physical layer security of wireless communications. Specifically, we first
design the RFDA-DM-AN scheme by randomly allocating frequencies to transmit
antennas, thereby achieving two-dimensionally (i.e., angle and range) secure
transmissions, and outperforming the state-of-the-art one-dimensional (i.e.,
angle) phase array (PA) based DM scheme. Then we develop the closed-form
expression of a lower bound on the ergodic secrecy capacity (ESC) of our
RFDA-DM-AN scheme. Based on the theoretical lower bound derived, we further
optimize the transmission power allocation between the useful signal and
artificial noise (AN) in order to enhance the ESC. Simulation results show that
1) our RFDA-DM-AN scheme achieves a higher secrecy capacity than that of the PA
based DM scheme, 2) the lower bound derived is shown to approach the ESC as the
number of transmit antennas N increases and precisely matches the ESC when N is
sufficiently large, and 3) the proposed optimum power allocation achieves the
highest ESC compared with other power allocations in the RFDA-DM-AN.
Francisco Lazaro, Cedomir Stefanovic
Comments: Accepted for publication in IEEE Communication Letters
Subjects: Information Theory (cs.IT)
In this paper we present a finite-length analysis of frameless ALOHA for a k
multi-user detection scenario, i.e., assuming the receiver can resolve
collisions of size k or smaller. The analysis is obtained via a dynamical
programming approach, and employed to optimize the scheme’s performance. We
also assess the optimized performance as function of k. Finally, we verify the
presented results through Monte Carlo simulations.
Yacong Ding, Bhaskar D. Rao
Comments: 31 pages, 8 figures, submitted
Subjects: Information Theory (cs.IT)
Downlink beamforming in FDD Massive MIMO systems is challenging due to the
large training and feedback overhead, which is proportional to the number of
antennas deployed at the base station, incurred by traditional downlink channel
estimation techniques. Leveraging the compressive sensing framework, compressed
channel estimation algorithm has been applied to obtain accurate channel
estimation with reduced training and feedback overhead, proportional to the
sparsity level of the channel. The prerequisite for using compressed channel
estimation is the existence of a sparse channel representation. This paper
proposes a new sparse channel model based on dictionary learning which adapts
to the cell characteristics and promotes a sparse representation. The learned
dictionary is able to more robustly and efficiently represent the channel and
improve downlink channel estimation accuracy. Furthermore, observing the
identical AOA/AOD between the uplink and downlink transmission, a joint uplink
and downlink dictionary learning and compressed channel estimation algorithm is
proposed to perform downlink channel estimation utilizing information from the
simpler uplink training, which further improves downlink channel estimation.
Numerical results are presented to show the robustness and efficiency of the
proposed dictionary learning based channel model and compressed channel
estimation algorithm.
Yang Hu, Yimin Liu, Xiqin Wang
Comments: 8 pages, 2 figures
Subjects: Information Theory (cs.IT)
This paper considers the problem of direction-of- arrival (DOA) estimation of
coherent signals on passive coprime arrays. We resort to the fourth-order
cumulants of the array signal in the proposed method. Using the property that
the individual sparse arrays are uniform, a generalized spatial smoothing
scheme is proposed to enhance the rank of the fourth- order cumulant matrix
(FCM). The subspace-based MUSIC algorithm applied to the spatial smoothed FCM
can successfully locate the DOAs of both independent and coherent signals. We
also provide a triple-coprime array structure that removes the false peaks
induced by coherent signals in the pseudo-spectrum. The effectiveness of the
new method is illustrated by simulation examples.
Nematollah Iri, Oliver Kosut
Comments: The paper has been submitted to IEEE Transactions on Information Theory
Subjects: Information Theory (cs.IT)
Universal source coding at short blocklengths is considered for an
exponential family of distributions. The emph{Type Size} code has previously
been shown to be optimal up to the third-order rate for universal compression
of all memoryless sources over finite alphabets. The Type Size code assigns
sequences ordered based on their type class sizes to binary strings ordered
lexicographically. To generalize this type class approach for parametric
sources, a natural scheme is to define two sequences to be in the same type
class if and only if they are equiprobable under any model in the parametric
class. This natural approach, however, is shown to be suboptimal. A variation
of the Type Size code is introduced, where type classes are defined based on
neighborhoods of minimal sufficient statistics. Asymptotics of the overflow
rate of this variation are derived and a converse result establishes its
optimality up to the third-order term. These results are derived for parametric
families of (i.i.d.) sources as well as Markov sources.
Mihailo Stojnic
Subjects: Optimization and Control (math.OC); Information Theory (cs.IT); Probability (math.PR)
Our companion work cite{Stojnicl1BnBxasymldp} considers random
under-determined linear systems with box-constrained sparse solutions and
provides an asymptotic analysis of a couple of modified (ell_1) heuristics
adjusted to handle such systems (we refer to these modifications of the
standard (ell_1) as binary and box (ell_1)). Our earlier work
cite{StojnicISIT2010binary} established that the binary (ell_1) does exhibit
the so-called phase-transition phenomenon (basically the same phenomenon
well-known through earlier considerations to be a key feature of the standard
(ell_1), see, e.g.
cite{DonohoPol,DonohoUnsigned,StojnicCSetam09,StojnicUpper10}). Moreover, in
cite{StojnicISIT2010binary}, we determined the precise location of the
co-called phase-transition (PT) curve. On the other hand, in
cite{Stojnicl1BnBxasymldp} we provide a much deeper understanding of the PTs
and do so through a large deviations principles (LDP) type of analysis. In this
paper we complement the results of cite{Stojnicl1BnBxasymldp} by leaving the
asymptotic regime naturally assumed in the PT and LDP considerations aside and
instead working in a finite dimensional setting. Along the same lines, we
provide for both, the binary and the box (ell_1), precise finite dimensional
analyses and essentially determine their ultimate statistical performance
characterizations. On top of that, we explain how the results created here can
be utilized in the asymptotic setting, considered in
cite{Stojnicl1BnBxasymldp}, as well. Finally, for the completeness, we also
present a collection of results obtained through numerical simulations and
observe that they are in a massive agreement with our theoretical calculations.
Mihailo Stojnic
Subjects: Probability (math.PR); Information Theory (cs.IT); Optimization and Control (math.OC)
In this paper we consider box constrained adaptations of (ell_1)
optimization heuristic when applied for solving random linear systems. These
are typically employed when on top of being sparse the systems’ solutions are
also known to be confined in a specific way to an interval on the real axis.
Two particular (ell_1) adaptations (to which we will refer as the
emph{binary} (ell_1) and emph{box} (ell_1)) will be discussed in great
detail. Many of their properties will be addressed with a special emphasis on
the so-called phase transitions (PT) phenomena and the large deviation
principles (LDP). We will fully characterize these through two different
mathematical approaches, the first one that is purely probabilistic in nature
and the second one that connects to high-dimensional geometry. Of particular
interest we will find that for many fairly hard mathematical problems a
collection of pretty elegant characterizations of their final solutions will
turn out to exist.
Roman Vershynin
Comments: Lectures given at 2016 PCMI Graduate Summer School in Mathematics of Data
Subjects: Probability (math.PR); Data Structures and Algorithms (cs.DS); Information Theory (cs.IT); Statistics Theory (math.ST)
Methods of high-dimensional probability play a central role in applications
for statistics, signal processing theoretical computer science and related
fields. These lectures present a sample of particularly useful tools of
high-dimensional probability, focusing on the classical and matrix Bernstein’s
inequality and the uniform matrix deviation inequality. We illustrate these
tools with applications for dimension reduction, network analysis, covariance
estimation, matrix completion and sparse signal recovery. The lectures are
geared towards beginning graduate students who have taken a rigorous course in
probability but may not have any experience in data science applications.
Hoi-To Wai, Anna Scaglione, Uzi Harush, Baruch Barzel, Amir Leshem
Comments: 20 pages, 6 figures
Subjects: Quantitative Methods (q-bio.QM); Information Theory (cs.IT); Molecular Networks (q-bio.MN); Machine Learning (stat.ML)
Reconstructing the causal network in a complex dynamical system plays a
crucial role in many applications, from sub-cellular biology to economic
systems. Here we focus on inferring gene regulation networks (GRNs) from
perturbation or gene deletion experiments. Despite their scientific merit, such
perturbation experiments are not often used for such inference due to their
costly experimental procedure, requiring significant resources to complete the
measurement of every single experiment. To overcome this challenge, we develop
the Robust IDentification of Sparse networks (RIDS) method that reconstructs
the GRN from a small number of perturbation experiments. Our method uses the
gene expression data observed in each experiment and translates that into a
steady state condition of the system’s nonlinear interaction dynamics. Applying
a sparse optimization criterion, we are able to extract the parameters of the
underlying weighted network, even from very few experiments. In fact, we
demonstrate analytically that, under certain conditions, the GRN can be
perfectly reconstructed using (K = Omega (d_{max})) perturbation experiments,
where (d_{max}) is the maximum in-degree of the GRN, a small value for
realistic sparse networks, indicating that RIDS can achieve high performance
with a scalable number of experiments. We test our method on both synthetic and
experimental data extracted from the DREAM5 network inference challenge. We
show that the RIDS achieves superior performance compared to the
state-of-the-art methods, while requiring as few as ~60% less experimental
data. Moreover, as opposed to almost all competing methods, RIDS allows us to
infer the directionality of the GRN links, allowing us to infer empirical GRNs,
without relying on the commonly provided list of transcription factors.
Mihailo Stojnic
Subjects: Optimization and Control (math.OC); Information Theory (cs.IT); Probability (math.PR)
In this paper we consider random linear under-determined systems with
block-sparse solutions. A standard subvariant of such systems, namely,
precisely the same type of systems without additional block structuring
requirement, gained a lot of popularity over the last decade. This is of course
in first place due to the success in mathematical characterization of an
(ell_1) optimization technique typically used for solving such systems,
initially achieved in cite{CRT,DOnoho06CS} and later on perfected in
cite{DonohoPol,DonohoUnsigned,StojnicCSetam09,StojnicUpper10}. The success
that we achieved in cite{StojnicCSetam09,StojnicUpper10} characterizing the
standard sparse solutions systems, we were then able to replicate in a sequence
of papers
cite{StojnicCSetamBlock09,StojnicUpperBlock10,StojnicICASSP09block,StojnicJSTSP09}
where instead of the standard (ell_1) optimization we utilized its an
(ell_2/ell_1) variant as a better fit for systems with block-sparse
solutions. All of these results finally settled the so-called threshold/phase
transitions phenomena (which naturally assume the asymptotic/large dimensional
scenario). Here, in addition to a few novel asymptotic considerations, we also
try to raise the level a bit, step a bit away from the asymptotics, and
consider the finite dimensions scenarios as well.