11,320 research outputs found
Revisiting Shor's quantum algorithm for computing general discrete logarithms
We heuristically demonstrate that Shor's algorithm for computing general
discrete logarithms, modified to allow the semi-classical Fourier transform to
be used with control qubit recycling, achieves a success probability of
approximately 60% to 82% in a single run. By slightly increasing the number of
group operations that are evaluated quantumly, and by performing a limited
search in the classical post-processing, we furthermore show how the algorithm
can be modified to achieve a success probability exceeding 99% in a single run.
We provide concrete heuristic estimates of the success probability of the
modified algorithm, as a function of the group order, the size of the search
space in the classical post-processing, and the additional number of group
operations evaluated quantumly. In analogy with our earlier works, we show how
the modified quantum algorithm may be simulated classically when the logarithm
and group order are both known. Furthermore, we show how slightly better
tradeoffs may be achieved, compared to our earlier works, if the group order is
known when computing the logarithm.Comment: The pre-print has been extended to show how slightly better tradeoffs
may be achieved, compared to our earlier works, if the group order is known.
A minor issue with an integration limit, that lead us to give a rough success
probability estimate of 60% to 70%, as opposed to 60% to 82%, has been
corrected. The heuristic and results reported in the original pre-print are
otherwise unaffecte
Compressed Text Indexes:From Theory to Practice!
A compressed full-text self-index represents a text in a compressed form and
still answers queries efficiently. This technology represents a breakthrough
over the text indexing techniques of the previous decade, whose indexes
required several times the size of the text. Although it is relatively new,
this technology has matured up to a point where theoretical research is giving
way to practical developments. Nonetheless this requires significant
programming skills, a deep engineering effort, and a strong algorithmic
background to dig into the research results. To date only isolated
implementations and focused comparisons of compressed indexes have been
reported, and they missed a common API, which prevented their re-use or
deployment within other applications.
The goal of this paper is to fill this gap. First, we present the existing
implementations of compressed indexes from a practitioner's point of view.
Second, we introduce the Pizza&Chili site, which offers tuned implementations
and a standardized API for the most successful compressed full-text
self-indexes, together with effective testbeds and scripts for their automatic
validation and test. Third, we show the results of our extensive experiments on
these codes with the aim of demonstrating the practical relevance of this novel
and exciting technology
Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks
A model, called the linear transform network (LTN), is proposed to analyze
the compression and estimation of correlated signals transmitted over directed
acyclic graphs (DAGs). An LTN is a DAG network with multiple source and
receiver nodes. Source nodes transmit subspace projections of random correlated
signals by applying reduced-dimension linear transforms. The subspace
projections are linearly processed by multiple relays and routed to intended
receivers. Each receiver applies a linear estimator to approximate a subset of
the sources with minimum mean squared error (MSE) distortion. The model is
extended to include noisy networks with power constraints on transmitters. A
key task is to compute all local compression matrices and linear estimators in
the network to minimize end-to-end distortion. The non-convex problem is solved
iteratively within an optimization framework using constrained quadratic
programs (QPs). The proposed algorithm recovers as special cases the regular
and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the
distortion region of multi-source, multi-receiver networks are given for linear
coding based on convex relaxations. Cut-set lower bounds are also given for any
coding strategy based on information theory. The distortion region and
compression-estimation tradeoffs are illustrated for different communication
demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal
Processin
Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples
This paper presents a novel power spectral density estimation technique for
band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The
technique employs multi-coset sampling and incorporates the advantages of
compressed sensing (CS) when the power spectrum is sparse, but applies to
sparse and nonsparse power spectra alike. The estimates are consistent
piecewise constant approximations whose resolutions (width of the piecewise
constant segments) are controlled by the periodicity of the multi-coset
sampling. We show that compressive estimates exhibit better tradeoffs among the
estimator's resolution, system complexity, and average sampling rate compared
to their noncompressive counterparts. For suitable sampling patterns,
noncompressive estimates are obtained as least squares solutions. Because of
the non-negativity of power spectra, compressive estimates can be computed by
seeking non-negative least squares solutions (provided appropriate sampling
patterns exist) instead of using standard CS recovery algorithms. This
flexibility suggests a reduction in computational overhead for systems
estimating both sparse and nonsparse power spectra because one algorithm can be
used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure
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