160,504 research outputs found
Distortion-Rate Function of Sub-Nyquist Sampled Gaussian Sources
The amount of information lost in sub-Nyquist sampling of a continuous-time
Gaussian stationary process is quantified. We consider a combined source coding
and sub-Nyquist reconstruction problem in which the input to the encoder is a
noisy sub-Nyquist sampled version of the analog source. We first derive an
expression for the mean squared error in the reconstruction of the process from
a noisy and information rate-limited version of its samples. This expression is
a function of the sampling frequency and the average number of bits describing
each sample. It is given as the sum of two terms: Minimum mean square error in
estimating the source from its noisy but otherwise fully observed sub-Nyquist
samples, and a second term obtained by reverse waterfilling over an average of
spectral densities associated with the polyphase components of the source. We
extend this result to multi-branch uniform sampling, where the samples are
available through a set of parallel channels with a uniform sampler and a
pre-sampling filter in each branch. Further optimization to reduce distortion
is then performed over the pre-sampling filters, and an optimal set of
pre-sampling filters associated with the statistics of the input signal and the
sampling frequency is found. This results in an expression for the minimal
possible distortion achievable under any analog to digital conversion scheme
involving uniform sampling and linear filtering. These results thus unify the
Shannon-Whittaker-Kotelnikov sampling theorem and Shannon rate-distortion
theory for Gaussian sources.Comment: Accepted for publication at the IEEE transactions on information
theor
Cryptanalysis of Two McEliece Cryptosystems Based on Quasi-Cyclic Codes
We cryptanalyse here two variants of the McEliece cryptosystem based on
quasi-cyclic codes. Both aim at reducing the key size by restricting the public
and secret generator matrices to be in quasi-cyclic form. The first variant
considers subcodes of a primitive BCH code. We prove that this variant is not
secure by finding and solving a linear system satisfied by the entries of the
secret permutation matrix.
The other variant uses quasi-cyclic low density parity-check codes. This
scheme was devised to be immune against general attacks working for McEliece
type cryptosystems based on low density parity-check codes by choosing in the
McEliece scheme more general one-to-one mappings than permutation matrices. We
suggest here a structural attack exploiting the quasi-cyclic structure of the
code and a certain weakness in the choice of the linear transformations that
hide the generator matrix of the code. Our analysis shows that with high
probability a parity-check matrix of a punctured version of the secret code can
be recovered in cubic time complexity in its length. The complete
reconstruction of the secret parity-check matrix of the quasi-cyclic low
density parity-check codes requires the search of codewords of low weight which
can be done with about operations for the specific parameters
proposed.Comment: Major corrections. This version supersedes previuos one
Hydrodynamic simulations with the Godunov SPH
We present results based on an implementation of the Godunov Smoothed
Particle Hydrodynamics (GSPH), originally developed by Inutsuka (2002), in the
GADGET-3 hydrodynamic code. We first review the derivation of the GSPH
discretization of the equations of moment and energy conservation, starting
from the convolution of these equations with the interpolating kernel. The two
most important aspects of the numerical implementation of these equations are
(a) the appearance of fluid velocity and pressure obtained from the solution of
the Riemann problem between each pair of particles, and (b the absence of an
artificial viscosity term. We carry out three different controlled
hydrodynamical three-dimensional tests, namely the Sod shock tube, the
development of Kelvin-Helmholtz instabilities in a shear flow test, and the
"blob" test describing the evolution of a cold cloud moving against a hot wind.
The results of our tests confirm and extend in a number of aspects those
recently obtained by Cha (2010): (i) GSPH provides a much improved description
of contact discontinuities, with respect to SPH, thus avoiding the appearance
of spurious pressure forces; (ii) GSPH is able to follow the development of
gas-dynamical instabilities, such as the Kevin--Helmholtz and the
Rayleigh-Taylor ones; (iii) as a result, GSPH describes the development of curl
structures in the shear-flow test and the dissolution of the cold cloud in the
"blob" test.
We also discuss in detail the effect on the performances of GSPH of changing
different aspects of its implementation. The results of our tests demonstrate
that GSPH is in fact a highly promising hydrodynamic scheme, also to be coupled
to an N-body solver, for astrophysical and cosmological applications.
[abridged]Comment: 19 pages, 13 figures, MNRAS accepted, high resolution version can be
obtained at
http://adlibitum.oats.inaf.it/borgani/html/papers/gsph_hydrosim.pd
Oversampling PCM techniques and optimum noise shapers for quantizing a class of nonbandlimited signals
We consider the efficient quantization of a class of nonbandlimited signals, namely, the class of discrete-time signals that can be recovered from their decimated version. The signals are modeled as the output of a single FIR interpolation filter (single band model) or, more generally, as the sum of the outputs of L FIR interpolation filters (multiband model). These nonbandlimited signals are oversampled, and it is therefore reasonable to expect that we can reap the same benefits of well-known efficient A/D techniques that apply only to bandlimited signals. We first show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of the signals. We can achieve a substantial decrease in bit rate by appropriately decimating the signals and then quantizing them. To further increase the effective quantizer resolution, noise shaping is introduced by optimizing prefilters and postfilters around the quantizer. We start with a scalar time-invariant quantizer and study two important cases of linear time invariant (LTI) filters, namely, the case where the postfilter is the inverse of the prefilter and the more general case where the postfilter is independent from the prefilter. Closed form expressions for the optimum filters and average minimum mean square error are derived in each case for both the single band and multiband models. The class of noise shaping filters and quantizers is then enlarged to include linear periodically time varying (LPTV)M filters and periodically time-varying quantizers of period M. We study two special cases in great detail
Coding gain in paraunitary analysis/synthesis systems
A formal proof that bit allocation results hold for the entire class of paraunitary subband coders is presented. The problem of finding an optimal paraunitary subband coder, so as to maximize the coding gain of the system, is discussed. The bit allocation problem is analyzed for the case of the paraunitary tree-structured filter banks, such as those used for generating orthonormal wavelets. The even more general case of nonuniform filter banks is also considered. In all cases it is shown that under optimal bit allocation, the variances of the errors introduced by each of the quantizers have to be equal. Expressions for coding gains for these systems are derived
- …