11,343 research outputs found
Continuity of Channel Parameters and Operations under Various DMC Topologies
We study the continuity of many channel parameters and operations under
various topologies on the space of equivalent discrete memoryless channels
(DMC). We show that mutual information, channel capacity, Bhattacharyya
parameter, probability of error of a fixed code, and optimal probability of
error for a given code rate and blocklength, are continuous under various DMC
topologies. We also show that channel operations such as sums, products,
interpolations, and Ar{\i}kan-style transformations are continuous.Comment: 31 pages. Submitted to IEEE Trans. Inform. Theory and in part to
ISIT201
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
Persistent Disagreement and Polarization in a Bayesian Setting
For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No
Topological Structures on DMC spaces
Two channels are said to be equivalent if they are degraded from each other.
The space of equivalent channels with input alphabet and output alphabet
can be naturally endowed with the quotient of the Euclidean topology by the
equivalence relation. A topology on the space of equivalent channels with fixed
input alphabet and arbitrary but finite output alphabet is said to be
natural if and only if it induces the quotient topology on the subspaces of
equivalent channels sharing the same output alphabet. We show that every
natural topology is -compact, separable and path-connected. On the
other hand, if , a Hausdorff natural topology is not Baire and it is
not locally compact anywhere. This implies that no natural topology can be
completely metrized if . The finest natural topology, which we call
the strong topology, is shown to be compactly generated, sequential and .
On the other hand, the strong topology is not first-countable anywhere, hence
it is not metrizable. We show that in the strong topology, a subspace is
compact if and only if it is rank-bounded and strongly-closed. We introduce a
metric distance on the space of equivalent channels which compares the noise
levels between channels. The induced metric topology, which we call the
noisiness topology, is shown to be natural. We also study topologies that are
inherited from the space of meta-probability measures by identifying channels
with their Blackwell measures. We show that the weak-* topology is exactly the
same as the noisiness topology and hence it is natural. We prove that if
, the total variation topology is not natural nor Baire, hence it is
not completely metrizable. Moreover, it is not locally compact anywhere.
Finally, we show that the Borel -algebra is the same for all Hausdorff
natural topologies.Comment: 43 pages, submitted to IEEE Trans. Inform. Theory and in part to
ISIT201
A novel CMB polarization likelihood package for large angular scales built from combined WMAP and Planck LFI legacy maps
We present a CMB large-scale polarization dataset obtained by combining WMAP
Ka, Q and V with Planck 70 GHz maps. We employ the legacy frequency maps
released by the WMAP and Planck collaborations and perform our own Galactic
foreground mitigation technique, which relies on Planck 353 GHz for polarized
dust and on Planck 30 GHz and WMAP K for polarized synchrotron. We derive a
single, optimally-noise-weighted, low-residual-foreground map and the
accompanying noise covariance matrix. These are shown, through
analysis, to be robust over an ample collection of Galactic masks. We use this
dataset, along with the Planck legacy Commander temperature solution, to build
a pixel-based low-resolution CMB likelihood package, whose robustness we test
extensively with the aid of simulations, finding excellent consistency. Using
this likelihood package alone, we constrain the optical depth to reionazation
at C.L., on 54\% of the sky. Adding the
Planck high- temperature and polarization legacy likelihood, the Planck
lensing likelihood and BAO observations we find
in a full CDM exploration. The
latter bounds are slightly less constraining than those obtained employing
\Planck\ HFI CMB data for large angle polarization, that only include EE
correlations. Our bounds are based on a largely independent dataset that does
include also TE correlations. They are generally well compatible with Planck
HFI preferring slightly higher values of . We make the low-resolution
Planck and WMAP joint dataset publicly available along with the accompanying
likelihood code.Comment: The WMAP+LFI likelihood module is available on
\http://www.fe.infn.it/u/pagano/low_ell_datasets/wmap_lfi_legacy
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