12,335 research outputs found
Extremes of error exponents
This paper determines the range of feasible values of standard error
exponents for binary-input memoryless symmetric channels of fixed capacity
and shows that extremes are attained by the binary symmetric and the binary
erasure channel. The proof technique also provides analogous extremes for other
quantities related to Gallager's function, such as the cutoff rate, the
Bhattacharyya parameter, and the channel dispersion
Extremes of Random Coding Error Exponents
Abstract-We show that Gallager's random coding error exponent of an arbitrary binary-input memoryless symmetric channel is upper-bounded by that of the binary erasure channel and lower-bounded by that of the binary-symmetric channel of the same capacity. We apply the result to find the extremes of the channel dispersion for the aforementioned class of channels. I. PRELIMINARIES We consider a classical communication scenario, where equiprobable messages m â {1, . . . , M} are to be transmitted over a binary-input memoryless symmetric channel described by the channel transition probabilities where n is the sequence length, X â X n , Y â Y n are the random variables corresponding to the channel input and output sequences, respectively, X is the random variable corresponding to the channel inputs taking values x on the binary alphabet X = {x 0 , x 1 }, Y is the random variable corresponding to the channel outputs taking values y on alphabet Y. Therefore, the channel is fully characterized by the probabilities P Y |X (y|x 0 ), P Y |X (y|x 1 ) for every y â Y. We consider symmetric channels [1], i.e., channels for which the channel transition probability matrix (rows corresponding to input values) is such that it can be partitioned in submatrices for which each row is a permutation of any other row and each column is a permutation of any other column. Strongly symmetric channels are those for which the channel transition probability matrix fulfils this permutation property (without partitioning into subsets). Examples of the above channels include the binary erasure channel (BEC) and the binary symmetric channel (BSC). This also extends to channels with continuous output alphabets, such as the binaryinput additive white Gaussian noise channel (BIAWGN). Each of the M messages is mapped into a codeword x(m) = x 1 (m), . . . , x n (m) with an encoder. The code C is the collection of all codewords. The code rate is R = 1 n log M . We consider maximum-likelihood (ML) decoding for which the estimated transmitted messagem is obtained as followĆ m = arg max The average probability of a message error is defined as where P e (m) is the probability of decoding messagem = m when message m was transmitted. A code rate R is said to be achievable if for every > 0 there exists a code of length n of rate not smaller than R such that P e < , for a suitably large n. The channel capacity C is the supremum of all achievable rates. For memoryless channels, the channel capacity is [2
Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient
In this paper we present and discuss results of Monte Carlo numerical
simulations of the two-dimensional Ising ferromagnet in contact with a heat
bath that intrinsically has a thermal gradient. The extremes of the magnet are
at temperatures , where is the Onsager critical temperature.
In this way one can observe a phase transition between an ordered phase
() by means of a single simulation. By
starting the simulations with fully disordered initial configurations with
magnetization corresponding to , which are then suddenly
annealed to a preset thermal gradient, we study the short-time critical dynamic
behavior of the system. Also, by setting a small initial magnetization ,
we study the critical initial increase of the order parameter. Furthermore, by
starting the simulations from fully ordered configurations, which correspond to
the ground state at T=0 and are subsequently quenched to a preset gradient, we
study the critical relaxation dynamics of the system. Additionally, we perform
stationary measurements () that are discussed in terms of
the standard finite-size scaling theory. We conclude that our numerical
simulation results of the Ising magnet in a thermal gradient, which are
rationalized in terms of both dynamic and standard scaling arguments, are fully
consistent with well established results obtained under equilibrium conditions
Electoral surveys influence on the voting processes: a cellular automata model
Nowadays, in societies threatened by atomization, selfishness, short-term
thinking, and alienation from political life, there is a renewed debate about
classical questions concerning the quality of democratic decision-making. In
this work a cellular automata (CA) model for the dynamics of free elections
based on the social impact theory is proposed. By using computer simulations,
power law distributions for the size of electoral clusters and decision time
have been obtained. The major role of broadcasted electoral surveys in guiding
opinion formation and stabilizing the ``{\it status quo}'' was demonstrated.
Furthermore, it was shown that in societies where these surveys are manipulated
within the universally accepted statistical error bars, even a majoritary
opposition could be hindered from reaching the power through the electoral
path.Comment: 15 pages, 9 figure
Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions
We investigate the domain growth and phase separation of
hydrodynamically-correct binary immiscible fluids of differing viscosity as a
function of minority phase concentration in both two and three spatial
dimensions using dissipative particle dynamics. We also examine the behavior of
equal-viscosity fluids and compare our results to similar lattice-gas
simulations in two dimensions.Comment: 34 pages (11 figures); accepted for publication in Phys. Rev.
Re-proving Channel Polarization Theorems: An Extremality and Robustness Analysis
The general subject considered in this thesis is a recently discovered coding
technique, polar coding, which is used to construct a class of error correction
codes with unique properties. In his ground-breaking work, Ar{\i}kan proved
that this class of codes, called polar codes, achieve the symmetric capacity
--- the mutual information evaluated at the uniform input distribution ---of
any stationary binary discrete memoryless channel with low complexity encoders
and decoders requiring in the order of operations in the
block-length . This discovery settled the long standing open problem left by
Shannon of finding low complexity codes achieving the channel capacity.
Polar coding settled an open problem in information theory, yet opened plenty
of challenging problems that need to be addressed. A significant part of this
thesis is dedicated to advancing the knowledge about this technique in two
directions. The first one provides a better understanding of polar coding by
generalizing some of the existing results and discussing their implications,
and the second one studies the robustness of the theory over communication
models introducing various forms of uncertainty or variations into the
probabilistic model of the channel.Comment: Preview of my PhD Thesis, EPFL, Lausanne, 2014. For the full version,
see http://people.epfl.ch/mine.alsan/publication
Extreme Value distribution for singular measures
In this paper we perform an analytical and numerical study of Extreme Value
distributions in discrete dynamical systems that have a singular measure. Using
the block maxima approach described in Faranda et al. [2011] we show that,
numerically, the Extreme Value distribution for these maps can be associated to
the Generalised Extreme Value family where the parameters scale with the
information dimension. The numerical analysis are performed on a few low
dimensional maps. For the middle third Cantor set and the Sierpinskij triangle
obtained using Iterated Function Systems, experimental parameters show a very
good agreement with the theoretical values. For strange attractors like Lozi
and H\`enon maps a slower convergence to the Generalised Extreme Value
distribution is observed. Even in presence of large statistics the observed
convergence is slower if compared with the maps which have an absolute
continuous invariant measure. Nevertheless and within the uncertainty computed
range, the results are in good agreement with the theoretical estimates
Scaling in DNA unzipping models: denaturated loops and end-segments as branches of a block copolymer network
For a model of DNA denaturation, exponents describing the distributions of
denaturated loops and unzipped end-segments are determined by exact enumeration
and by Monte Carlo simulations in two and three dimensions. The loop
distributions are consistent with first order thermal denaturation in both
cases. Results for end-segments show a coexistence of two distinct power laws
in the relative distributions, which is not foreseen by a recent approach in
which DNA is treated as a homogeneous network of linear polymer segments. This
unexpected feature, and the discrepancies with such an approach, are explained
in terms of a refined scaling picture in which a precise distinction is made
between network branches representing single stranded and effective double
stranded segments.Comment: 8 pages, 8 figure
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