3,741 research outputs found
Multi Terminal Probabilistic Compressed Sensing
In this paper, the `Approximate Message Passing' (AMP) algorithm, initially
developed for compressed sensing of signals under i.i.d. Gaussian measurement
matrices, has been extended to a multi-terminal setting (MAMP algorithm). It
has been shown that similar to its single terminal counterpart, the behavior of
MAMP algorithm is fully characterized by a `State Evolution' (SE) equation for
large block-lengths. This equation has been used to obtain the rate-distortion
curve of a multi-terminal memoryless source. It is observed that by spatially
coupling the measurement matrices, the rate-distortion curve of MAMP algorithm
undergoes a phase transition, where the measurement rate region corresponding
to a low distortion (approximately zero distortion) regime is fully
characterized by the joint and conditional Renyi information dimension (RID) of
the multi-terminal source. This measurement rate region is very similar to the
rate region of the Slepian-Wolf distributed source coding problem where the RID
plays a role similar to the discrete entropy.
Simulations have been done to investigate the empirical behavior of MAMP
algorithm. It is observed that simulation results match very well with
predictions of SE equation for reasonably large block-lengths.Comment: 11 pages, 13 figures. arXiv admin note: text overlap with
arXiv:1112.0708 by other author
Polarization of the Renyi Information Dimension with Applications to Compressed Sensing
In this paper, we show that the Hadamard matrix acts as an extractor over the
reals of the Renyi information dimension (RID), in an analogous way to how it
acts as an extractor of the discrete entropy over finite fields. More
precisely, we prove that the RID of an i.i.d. sequence of mixture random
variables polarizes to the extremal values of 0 and 1 (corresponding to
discrete and continuous distributions) when transformed by a Hadamard matrix.
Further, we prove that the polarization pattern of the RID admits a closed form
expression and follows exactly the Binary Erasure Channel (BEC) polarization
pattern in the discrete setting. We also extend the results from the single- to
the multi-terminal setting, obtaining a Slepian-Wolf counterpart of the RID
polarization. We discuss applications of the RID polarization to Compressed
Sensing of i.i.d. sources. In particular, we use the RID polarization to
construct a family of deterministic -valued sensing matrices for
Compressed Sensing. We run numerical simulations to compare the performance of
the resulting matrices with that of random Gaussian and random Hadamard
matrices. The results indicate that the proposed matrices afford competitive
performances while being explicitly constructed.Comment: 12 pages, 2 figure
Networking - A Statistical Physics Perspective
Efficient networking has a substantial economic and societal impact in a
broad range of areas including transportation systems, wired and wireless
communications and a range of Internet applications. As transportation and
communication networks become increasingly more complex, the ever increasing
demand for congestion control, higher traffic capacity, quality of service,
robustness and reduced energy consumption require new tools and methods to meet
these conflicting requirements. The new methodology should serve for gaining
better understanding of the properties of networking systems at the macroscopic
level, as well as for the development of new principled optimization and
management algorithms at the microscopic level. Methods of statistical physics
seem best placed to provide new approaches as they have been developed
specifically to deal with non-linear large scale systems. This paper aims at
presenting an overview of tools and methods that have been developed within the
statistical physics community and that can be readily applied to address the
emerging problems in networking. These include diffusion processes, methods
from disordered systems and polymer physics, probabilistic inference, which
have direct relevance to network routing, file and frequency distribution, the
exploration of network structures and vulnerability, and various other
practical networking applications.Comment: (Review article) 71 pages, 14 figure
Cross-Sender Bit-Mixing Coding
Scheduling to avoid packet collisions is a long-standing challenge in
networking, and has become even trickier in wireless networks with multiple
senders and multiple receivers. In fact, researchers have proved that even {\em
perfect} scheduling can only achieve . Here
is the number of nodes in the network, and is the {\em medium
utilization rate}. Ideally, one would hope to achieve ,
while avoiding all the complexities in scheduling. To this end, this paper
proposes {\em cross-sender bit-mixing coding} ({\em BMC}), which does not rely
on scheduling. Instead, users transmit simultaneously on suitably-chosen slots,
and the amount of overlap in different user's slots is controlled via coding.
We prove that in all possible network topologies, using BMC enables us to
achieve . We also prove that the space and time
complexities of BMC encoding/decoding are all low-order polynomials.Comment: Published in the International Conference on Information Processing
in Sensor Networks (IPSN), 201
Massive MIMO for Internet of Things (IoT) Connectivity
Massive MIMO is considered to be one of the key technologies in the emerging
5G systems, but also a concept applicable to other wireless systems. Exploiting
the large number of degrees of freedom (DoFs) of massive MIMO essential for
achieving high spectral efficiency, high data rates and extreme spatial
multiplexing of densely distributed users. On the one hand, the benefits of
applying massive MIMO for broadband communication are well known and there has
been a large body of research on designing communication schemes to support
high rates. On the other hand, using massive MIMO for Internet-of-Things (IoT)
is still a developing topic, as IoT connectivity has requirements and
constraints that are significantly different from the broadband connections. In
this paper we investigate the applicability of massive MIMO to IoT
connectivity. Specifically, we treat the two generic types of IoT connections
envisioned in 5G: massive machine-type communication (mMTC) and ultra-reliable
low-latency communication (URLLC). This paper fills this important gap by
identifying the opportunities and challenges in exploiting massive MIMO for IoT
connectivity. We provide insights into the trade-offs that emerge when massive
MIMO is applied to mMTC or URLLC and present a number of suitable communication
schemes. The discussion continues to the questions of network slicing of the
wireless resources and the use of massive MIMO to simultaneously support IoT
connections with very heterogeneous requirements. The main conclusion is that
massive MIMO can bring benefits to the scenarios with IoT connectivity, but it
requires tight integration of the physical-layer techniques with the protocol
design.Comment: Submitted for publicatio
Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
In this work the dynamic compressive sensing (CS) problem of recovering
sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear
measurements is explored from a Bayesian perspective. While there has been a
handful of previously proposed Bayesian dynamic CS algorithms in the
literature, the ability to perform inference on high-dimensional problems in a
computationally efficient manner remains elusive. In response, we propose a
probabilistic dynamic CS signal model that captures both amplitude and support
correlation structure, and describe an approximate message passing algorithm
that performs soft signal estimation and support detection with a computational
complexity that is linear in all problem dimensions. The algorithm, DCS-AMP,
can perform either causal filtering or non-causal smoothing, and is capable of
learning model parameters adaptively from the data through an
expectation-maximization learning procedure. We provide numerical evidence that
DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety
of operating conditions. We further describe the result of applying DCS-AMP to
two real dynamic CS datasets, as well as a frequency estimation task, to
bolster our claim that DCS-AMP is capable of offering state-of-the-art
performance and speed on real-world high-dimensional problems.Comment: 32 pages, 7 figure
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Wireless Communications in the Era of Big Data
The rapidly growing wave of wireless data service is pushing against the
boundary of our communication network's processing power. The pervasive and
exponentially increasing data traffic present imminent challenges to all the
aspects of the wireless system design, such as spectrum efficiency, computing
capabilities and fronthaul/backhaul link capacity. In this article, we discuss
the challenges and opportunities in the design of scalable wireless systems to
embrace such a "bigdata" era. On one hand, we review the state-of-the-art
networking architectures and signal processing techniques adaptable for
managing the bigdata traffic in wireless networks. On the other hand, instead
of viewing mobile bigdata as a unwanted burden, we introduce methods to
capitalize from the vast data traffic, for building a bigdata-aware wireless
network with better wireless service quality and new mobile applications. We
highlight several promising future research directions for wireless
communications in the mobile bigdata era.Comment: This article is accepted and to appear in IEEE Communications
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