386 research outputs found
Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion
A spectrally sparse signal of order is a mixture of damped or
undamped complex sinusoids. This paper investigates the problem of
reconstructing spectrally sparse signals from a random subset of regular
time domain samples, which can be reformulated as a low rank Hankel matrix
completion problem. We introduce an iterative hard thresholding (IHT) algorithm
and a fast iterative hard thresholding (FIHT) algorithm for efficient
reconstruction of spectrally sparse signals via low rank Hankel matrix
completion. Theoretical recovery guarantees have been established for FIHT,
showing that number of samples are sufficient for exact
recovery with high probability. Empirical performance comparisons establish
significant computational advantages for IHT and FIHT. In particular, numerical
simulations on D arrays demonstrate the capability of FIHT on handling large
and high-dimensional real data
Variational Bayesian Inference of Line Spectra
In this paper, we address the fundamental problem of line spectral estimation
in a Bayesian framework. We target model order and parameter estimation via
variational inference in a probabilistic model in which the frequencies are
continuous-valued, i.e., not restricted to a grid; and the coefficients are
governed by a Bernoulli-Gaussian prior model turning model order selection into
binary sequence detection. Unlike earlier works which retain only point
estimates of the frequencies, we undertake a more complete Bayesian treatment
by estimating the posterior probability density functions (pdfs) of the
frequencies and computing expectations over them. Thus, we additionally capture
and operate with the uncertainty of the frequency estimates. Aiming to maximize
the model evidence, variational optimization provides analytic approximations
of the posterior pdfs and also gives estimates of the additional parameters. We
propose an accurate representation of the pdfs of the frequencies by mixtures
of von Mises pdfs, which yields closed-form expectations. We define the
algorithm VALSE in which the estimates of the pdfs and parameters are
iteratively updated. VALSE is a gridless, convergent method, does not require
parameter tuning, can easily include prior knowledge about the frequencies and
provides approximate posterior pdfs based on which the uncertainty in line
spectral estimation can be quantified. Simulation results show that accounting
for the uncertainty of frequency estimates, rather than computing just point
estimates, significantly improves the performance. The performance of VALSE is
superior to that of state-of-the-art methods and closely approaches the
Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on
Signal Processin
Extrinsic models for the dielectric response of CaCu{3}Ti{4}O{12}
The large, temperature-independent, low-frequency dielectric constant
recently observed in single-crystal CaCu{3}Ti{4}O{12} is most plausibly
interpreted as arising from spatial inhomogenities of its local dielectric
response. Probable sources of inhomogeneity are the various domain boundaries
endemic in such materials: twin, Ca-ordering, and antiphase boundaries. The
material in and neighboring such boundaries can be insulating or conducting. We
construct a decision tree for the resulting six possible morphologies, and
derive or present expressions for the dielectric constant for models of each
morphology. We conclude that all six morphologies can yield dielectric behavior
consistent with observations and suggest further experiments to distinguish
among them.Comment: 9 pages, with 1 postscript figure embedded. Uses REVTEX and epsf
macros. Also available at
http://www.physics.rutgers.edu/~dhv/preprints/mc_ext/index.htm
Revisiting Structure Graphs: Applications to CBC-MAC and EMAC
In Crypto\u2705, Bellare et al. proved an bound for the PRF (pseudorandom function) security of the CBC-MAC based on an -bit random permutation , provided . Here an adversary can make at most prefix-free queries each having at most many ``blocks\u27\u27 (elements of ). In the same paper an bound for EMAC (or encrypted CBC-MAC) was proved, provided . Both proofs are based on {\bf structure graphs} representing all collisions among ``intermediate inputs\u27\u27 to during the computation of CBC. The problem of bounding PRF-advantage is shown to be reduced to bounding the number of structure graphs satisfying certain collision patterns. In the present paper, we show that the Lemma 10 in the Crypto \u2705 paper, stating an important result on structure graphs, is incorrect. This is due to the fact that the authors overlooked certain structure graphs. This invalidates the proofs of the PRF bounds. In ICALP \u2706, Pietrzak improved the bound for EMAC by showing a tight bound under the restriction that . As he used the same flawed lemma, this proof also becomes invalid. In this paper, we have revised and sometimes simplified these proofs. We revisit structure graphs in a slightly different mathematical language and provide a complete characterization of certain types of structure graphs. Using this characterization, we show that PRF security of CBC-MAC is about provided where is the total number of blocks in all queries. We also recover tight bound for PRF security of EMAC with a much relaxed constraint () than the original ()
Large-Scale Optical Neural Networks based on Photoelectric Multiplication
Recent success in deep neural networks has generated strong interest in
hardware accelerators to improve speed and energy consumption. This paper
presents a new type of photonic accelerator based on coherent detection that is
scalable to large () networks and can be operated at high (GHz)
speeds and very low (sub-aJ) energies per multiply-and-accumulate (MAC), using
the massive spatial multiplexing enabled by standard free-space optical
components. In contrast to previous approaches, both weights and inputs are
optically encoded so that the network can be reprogrammed and trained on the
fly. Simulations of the network using models for digit- and
image-classification reveal a "standard quantum limit" for optical neural
networks, set by photodetector shot noise. This bound, which can be as low as
50 zJ/MAC, suggests performance below the thermodynamic (Landauer) limit for
digital irreversible computation is theoretically possible in this device. The
proposed accelerator can implement both fully-connected and convolutional
networks. We also present a scheme for back-propagation and training that can
be performed in the same hardware. This architecture will enable a new class of
ultra-low-energy processors for deep learning.Comment: Text: 10 pages, 5 figures, 1 table. Supplementary: 8 pages, 5,
figures, 2 table
On The Exact Security of Message Authentication Using Pseudorandom Functions
Traditionally, modes of Message Authentication Codes(MAC) such as Cipher Block Chaining (CBC) are instantiated using block ciphers or keyed Pseudo Random Permutations(PRP). However, one can also use domain preserving keyed Pseudo Random Functions(PRF) to instantiate MAC modes. The very first security proof of CBC-MAC [BKR00], essentially modeled the PRP as a PRF. Until now very little work has been done to investigate the difference between PRP vs PRF instantiations. Only known result is the rather loose folklore PRP-PRF transition of any PRP based security proof, which looses a factor of Ο( σ2/2n ) (domain of PRF/PRP is {0, 1}n and adversary makes σ many PRP/PRF calls in total). This loss is significant, considering the fact tight Θ( q2/2n ) security bounds have been known for PRP based EMAC and ECBC constructions (where q is the total number of adversary queries). In this work, we show for many variations of encrypted CBC MACs (i.e. EMAC, ECBC, FCBC, XCBC and TCBC), random function based instantiation has a security bound Ο( qσ/2n ). This is a significant improvement over the folklore PRP/PRF transition. We also show this bound is optimal by providing an attack against the underlying PRF based CBC construction. This shows for EMAC, ECBC and FCBC, PRP instantiations are substantially more secure than PRF instantiations. Where as, for XCBC and TMAC, PRP instantiations are at least as secure as PRF instantiations
A MAC Mode for Lightweight Block Ciphers
status: accepte
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