Capacity Upper Bounds for Deletion-Type Channels

We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the classical deletion channel, we give a special attention to the Poisson-repeat channel introduced by Mitzenmacher and Drinea (IEEE Transactions on Information Theory, 2006). Our framework can be applied to obtain capacity upper bounds for any repetition distribution (the deletion and Poisson-repeat channels corresponding to the special cases of Bernoulli and Poisson distributions). Our techniques essentially reduce the task of proving capacity upper bounds to maximizing a univariate, real-valued, and often concave function over a bounded interval. We show the following: 1. The capacity of the binary deletion channel with deletion probability $d$ is at most $(1-d)\log\varphi$ for $d\geq 1/2$, and, assuming the capacity function is convex, is at most $1-d\log(4/\varphi)$ for $d<1/2$, where $\varphi=(1+\sqrt{5})/2$ is the golden ratio. This is the first nontrivial capacity upper bound for any value of $d$ outside the limiting case $d\to 0$ that is fully explicit and proved without computer assistance. 2. We derive the first set of capacity upper bounds for the Poisson-repeat channel. 3. We derive several novel upper bounds on the capacity of the deletion channel. All upper bounds are maximums of efficiently computable, and concave, univariate real functions over a bounded domain. In turn, we upper bound these functions in terms of explicit elementary and standard special functions, whose maximums can be found even more efficiently (and sometimes, analytically, for example for $d=1/2$). Along the way, we develop several new techniques of potentially independent interest in information theory, probability, and mathematical analysis.Comment: Minor edits, In Proceedings of 50th Annual ACM SIGACT Symposium on the Theory of Computing (STOC), 201

Angle-resolved photoelectron spectrometry studies of the autoionization of the 2s22p 2P triply excited state of atomic lithium: experimental results and R-matrix calculations

We have measured the angle-resolved energy dependence of the electrons emitted over the energy range of the triply excited 2s22p2P lithium resonance using synchrotron radiation. We have also calculated the behavior of the angular distribution parameter β using the R-matrix approximation. Experimental and theoretical results are in good agreement and show deep minima in the 1s2p1,3P ionic channels. The energy at which the minima occur does not coincide with the resonance energy, but is shifted towards higher energy

Malunion after midshaft clavicle fractures in adults: The current view on clavicular malunion in the literature

This is an overview of the current literature on malunion after midshaft clavicle fracture. Anatomy, trauma mechanism, classification, incidence, symptoms, prevention, and treatment options are all discussed. The conclusion is that clavicle malunion is a distinct clinical entity that can be treated successfully

Antecedents of hospital admission for deliberate self-harm from a 14-year follow-up study using data-linkage

Antecedents of hospital admission for deliberate self-harm from a 14-year follow-up study using data-linkageFrancis Mitrou1 email, Jennifer Gaudie1 email, David Lawrence1,2 email, Sven R Silburn1,2 email, Fiona J Stanley1 email and Stephen R Zubrick1,2 email1 Telethon Institute for Child Health Research, Centre for Child Health Research, The University of Western Australia. PO Box 855, West Perth, WA. 6872, Australia2 Centre for Developmental Health, Curtin Health Innovation Research Institute, Curtin University of Technology, Perth, Western Australia, Australiaauthor email corresponding author emailBMC Psychiatry 2010, 10:82doi:10.1186/1471-244X-10-82The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-244X/10/82Received: 22 April 2010Accepted: 18 October 2010Published: 18 October 2010© 2010 Mitrou et al; licensee BioMed Central Ltd.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

REFERENCES

[14] J. W. Woods and T. Naveen, &amp;quot;A filter based bit allocation scheme for subban