59 research outputs found
On privacy amplification, lossy compression, and their duality to channel coding
We examine the task of privacy amplification from information-theoretic and
coding-theoretic points of view. In the former, we give a one-shot
characterization of the optimal rate of privacy amplification against classical
adversaries in terms of the optimal type-II error in asymmetric hypothesis
testing. This formulation can be easily computed to give finite-blocklength
bounds and turns out to be equivalent to smooth min-entropy bounds by Renner
and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [ISIT 2013], as well as a
bound in terms of the divergence by Yang, Schaefer, and Poor
[arXiv:1706.03866 [cs.IT]]. In the latter, we show that protocols for privacy
amplification based on linear codes can be easily repurposed for channel
simulation. Combined with known relations between channel simulation and lossy
source coding, this implies that privacy amplification can be understood as a
basic primitive for both channel simulation and lossy compression. Applied to
symmetric channels or lossy compression settings, our construction leads to
proto- cols of optimal rate in the asymptotic i.i.d. limit. Finally, appealing
to the notion of channel duality recently detailed by us in [IEEE Trans. Info.
Theory 64, 577 (2018)], we show that linear error-correcting codes for
symmetric channels with quantum output can be transformed into linear lossy
source coding schemes for classical variables arising from the dual channel.
This explains a "curious duality" in these problems for the (self-dual) erasure
channel observed by Martinian and Yedidia [Allerton 2003; arXiv:cs/0408008] and
partly anticipates recent results on optimal lossy compression by polar and
low-density generator matrix codes.Comment: v3: updated to include equivalence of the converse bound with smooth
entropy formulations. v2: updated to include comparison with the one-shot
bounds of arXiv:1706.03866. v1: 11 pages, 4 figure
One-Shot Mutual Covering Lemma and Marton's Inner Bound with a Common Message
By developing one-shot mutual covering lemmas, we derive a one-shot
achievability bound for broadcast with a common message which recovers Marton's
inner bound (with three auxiliary random variables) in the i.i.d.~case. The
encoder employed is deterministic. Relationship between the mutual covering
lemma and a new type of channel resolvability problem is discussed.Comment: 6 pages; extended version of ISIT pape
One-point fluctuation analysis of the high-energy neutrino sky
We perform the first one-point fluctuation analysis of the high-energy
neutrino sky. This method reveals itself to be especially suited to
contemporary neutrino data, as it allows to study the properties of the
astrophysical components of the high-energy flux detected by the IceCube
telescope, even with low statistics and in the absence of point source
detection. Besides the veto-passing atmospheric foregrounds, we adopt a simple
model of the high-energy neutrino background by assuming two main
extra-galactic components: star-forming galaxies and blazars. By leveraging
multi-wavelength data from Herschel and Fermi, we predict the spectral and
anisotropic probability distributions for their expected neutrino counts in
IceCube. We find that star-forming galaxies are likely to remain a diffuse
background due to the poor angular resolution of IceCube, and we determine an
upper limit on the number of shower events that can reasonably be associated to
blazars. We also find that upper limits on the contribution of blazars to the
measured flux are unfavourably affected by the skewness of the blazar flux
distribution. One-point event clustering and likelihood analyses of the IceCube
HESE data suggest that this method has the potential to dramatically improve
over more conventional model-based analyses, especially for the next generation
of neutrino telescopes.Comment: 41 pages, 6 figures, 2 tables; different blazar model than v1 but
same result
Smoothing of binary codes, uniform distributions, and applications
The action of a noise operator on a code transforms it into a distribution on
the respective space. Some common examples from information theory include
Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting
on a lattice in the Euclidean space. We aim to characterize the cases when the
output distribution is close to the uniform distribution on the space, as
measured by R{\'e}nyi divergence of order . A version of
this question is known as the channel resolvability problem in information
theory, and it has implications for security guarantees in wiretap channels,
error correction, discrepancy, worst-to-average case complexity reductions, and
many other problems.
Our work quantifies the requirements for asymptotic uniformity (perfect
smoothing) and identifies explicit code families that achieve it under the
action of the Bernoulli and ball noise operators on the code. We derive
expressions for the minimum rate of codes required to attain asymptotically
perfect smoothing. In proving our results, we leverage recent results from
harmonic analysis of functions on the Hamming space. Another result pertains to
the use of code families in Wyner's transmission scheme on the binary wiretap
channel. We identify explicit families that guarantee strong secrecy when
applied in this scheme, showing that nested Reed-Muller codes can transmit
messages reliably and securely over a binary symmetric wiretap channel with a
positive rate. Finally, we establish a connection between smoothing and error
correction in the binary symmetric channel
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