4,050 research outputs found
Complex-Valued Random Vectors and Channels: Entropy, Divergence, and Capacity
Recent research has demonstrated significant achievable performance gains by
exploiting circularity/non-circularity or propeness/improperness of
complex-valued signals. In this paper, we investigate the influence of these
properties on important information theoretic quantities such as entropy,
divergence, and capacity. We prove two maximum entropy theorems that strengthen
previously known results. The proof of the former theorem is based on the
so-called circular analog of a given complex-valued random vector. Its
introduction is supported by a characterization theorem that employs a minimum
Kullback-Leibler divergence criterion. In the proof of latter theorem, on the
other hand, results about the second-order structure of complex-valued random
vectors are exploited. Furthermore, we address the capacity of multiple-input
multiple-output (MIMO) channels. Regardless of the specific distribution of the
channel parameters (noise vector and channel matrix, if modeled as random), we
show that the capacity-achieving input vector is circular for a broad range of
MIMO channels (including coherent and noncoherent scenarios). Finally, we
investigate the situation of an improper and Gaussian distributed noise vector.
We compute both capacity and capacity-achieving input vector and show that
improperness increases capacity, provided that the complementary covariance
matrix is exploited. Otherwise, a capacity loss occurs, for which we derive an
explicit expression.Comment: 33 pages, 1 figure, slightly modified version of first paper revision
submitted to IEEE Trans. Inf. Theory on October 31, 201
Spread spectrum-based video watermarking algorithms for copyright protection
Merged with duplicate record 10026.1/2263 on 14.03.2017 by CS (TIS)Digital technologies know an unprecedented expansion in the last years. The consumer can
now benefit from hardware and software which was considered state-of-the-art several years
ago. The advantages offered by the digital technologies are major but the same digital
technology opens the door for unlimited piracy. Copying an analogue VCR tape was certainly
possible and relatively easy, in spite of various forms of protection, but due to the analogue
environment, the subsequent copies had an inherent loss in quality. This was a natural way of
limiting the multiple copying of a video material. With digital technology, this barrier
disappears, being possible to make as many copies as desired, without any loss in quality
whatsoever. Digital watermarking is one of the best available tools for fighting this threat.
The aim of the present work was to develop a digital watermarking system compliant with the
recommendations drawn by the EBU, for video broadcast monitoring. Since the watermark
can be inserted in either spatial domain or transform domain, this aspect was investigated and
led to the conclusion that wavelet transform is one of the best solutions available. Since
watermarking is not an easy task, especially considering the robustness under various attacks
several techniques were employed in order to increase the capacity/robustness of the system:
spread-spectrum and modulation techniques to cast the watermark, powerful error correction
to protect the mark, human visual models to insert a robust mark and to ensure its invisibility.
The combination of these methods led to a major improvement, but yet the system wasn't
robust to several important geometrical attacks. In order to achieve this last milestone, the
system uses two distinct watermarks: a spatial domain reference watermark and the main
watermark embedded in the wavelet domain. By using this reference watermark and techniques
specific to image registration, the system is able to determine the parameters of the attack and
revert it. Once the attack was reverted, the main watermark is recovered. The final result is a
high capacity, blind DWr-based video watermarking system, robust to a wide range of attacks.BBC Research & Developmen
Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics
The mutual information between a complex-valued channel input and its
complex-valued output is decomposed into four parts based on polar coordinates:
an amplitude term, a phase term, and two mixed terms. Numerical results for the
additive white Gaussian noise (AWGN) channel with various inputs show that, at
high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the
mixed terms. For the AWGN channel with a Gaussian input, analytical expressions
are derived for high SNR. The decomposition method is applied to partially
coherent channels and a property of such channels called "spectral loss" is
developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be
one effect that needs to be taken into account to explain the behavior of the
capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on
Information Theor
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
Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey
This paper provides a comprehensive review of the domain of physical layer
security in multiuser wireless networks. The essential premise of
physical-layer security is to enable the exchange of confidential messages over
a wireless medium in the presence of unauthorized eavesdroppers without relying
on higher-layer encryption. This can be achieved primarily in two ways: without
the need for a secret key by intelligently designing transmit coding
strategies, or by exploiting the wireless communication medium to develop
secret keys over public channels. The survey begins with an overview of the
foundations dating back to the pioneering work of Shannon and Wyner on
information-theoretic security. We then describe the evolution of secure
transmission strategies from point-to-point channels to multiple-antenna
systems, followed by generalizations to multiuser broadcast, multiple-access,
interference, and relay networks. Secret-key generation and establishment
protocols based on physical layer mechanisms are subsequently covered.
Approaches for secrecy based on channel coding design are then examined, along
with a description of inter-disciplinary approaches based on game theory and
stochastic geometry. The associated problem of physical-layer message
authentication is also introduced briefly. The survey concludes with
observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with
arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials,
201
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