55,120 research outputs found
Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities
This monograph presents a unified treatment of single- and multi-user
problems in Shannon's information theory where we depart from the requirement
that the error probability decays asymptotically in the blocklength. Instead,
the error probabilities for various problems are bounded above by a
non-vanishing constant and the spotlight is shone on achievable coding rates as
functions of the growing blocklengths. This represents the study of asymptotic
estimates with non-vanishing error probabilities.
In Part I, after reviewing the fundamentals of information theory, we discuss
Strassen's seminal result for binary hypothesis testing where the type-I error
probability is non-vanishing and the rate of decay of the type-II error
probability with growing number of independent observations is characterized.
In Part II, we use this basic hypothesis testing result to develop second- and
sometimes, even third-order asymptotic expansions for point-to-point
communication. Finally in Part III, we consider network information theory
problems for which the second-order asymptotics are known. These problems
include some classes of channels with random state, the multiple-encoder
distributed lossless source coding (Slepian-Wolf) problem and special cases of
the Gaussian interference and multiple-access channels. Finally, we discuss
avenues for further research.Comment: Further comments welcom
A Formula for the Capacity of the General Gel'fand-Pinsker Channel
We consider the Gel'fand-Pinsker problem in which the channel and state are
general, i.e., possibly non-stationary, non-memoryless and non-ergodic. Using
the information spectrum method and a non-trivial modification of the piggyback
coding lemma by Wyner, we prove that the capacity can be expressed as an
optimization over the difference of a spectral inf- and a spectral sup-mutual
information rate. We consider various specializations including the case where
the channel and state are memoryless but not necessarily stationary.Comment: Accepted to the IEEE Transactions on Communication
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A modularized electronic payment system for agent-based e-commerce
With the explosive growth of the Internet, electronic-commerce (e-commerce) is an increasingly important segment of commercial activities on the web. The Secure Agent Fabrication, Evolution & Roaming (SAFER) architecture was proposed to further facilitate e-commerce using agent technology. In this paper, the electronic payment aspect of SAFER will be explored. The Secure Electronic Transaction (SET) protocol and E-Cash were selected as the bases for the electronic payment system implementation. The various modules of the payment system and how they interface with each other are shown. An extensible implementation done using JavaTM will also be elaborated. This application incorporates agent roaming functionality and the ability to conduct e-commerce transactions and carry out intelligent e-payment procedures
Second-Order Asymptotics for the Discrete Memoryless MAC with Degraded Message Sets
This paper studies the second-order asymptotics of the discrete memoryless
multiple-access channel with degraded message sets. For a fixed average error
probability and an arbitrary point on the boundary of the
capacity region, we characterize the speed of convergence of rate pairs that
converge to that point for codes that have asymptotic error probability no
larger than , thus complementing an analogous result given previously
for the Gaussian setting.Comment: 5 Pages, 1 Figure. Follow-up paper of http://arxiv.org/abs/1310.1197.
Accepted to ISIT 201
Voting on Punishment Systems Within a Heterogeneous Group
We consider a voluntary contributions game, in which players may punish others after contributions are made and observed. The productivity of contributions, as captured in the marginal-per-capita return, differs among individuals, so that there are two types: high and low productivity. Every two or eight periods, depending on the treatment, individuals vote on a punishment regime, in which certain individuals are permitted, but not required, to have punishment directed toward them. The punishment system can condition on type and contribution history. The results indicate that the most effective regime, in terms of contributions and earnings, is one that allows punishment of low contributors only, regardless of productivity. Nevertheless, only a minority of sessions converge to this system, indicating a tendency for the voting process to lead to suboptimal institutional choice.Voting;Punishment;Voluntary Contributions;Heterogeneity;Experiment
Star Formation at Zero and Very Low Metallicities
We describe how star formation is expected to proceed in the early metal-free
Universe, focusing on the very first generations of stars. We then discuss how
the star formation process may change as the effects of metallicity, external
radiative feedback, and magnetic and turbulent support of the gas become more
important. The very first stars (Pop III.1) have relatively simple initial
conditions set by cosmology and the cooling properties of primordial gas. We
describe the evolution of these stars as they grow in mass by accretion from
their surrounding gas cores and how the accretion process is affected and
eventually terminated by radiative feedback processes, especially HII region
expansion and disk photoevaporation. The ability of the protostar and its disk
to generate dynamically important magnetic fields is reviewed and their effects
discussed. Pop III.1 star formation is likely to produce massive (~100-200Msun)
stars that then influence their surroundings via ionization, stellar winds, and
supernovae. These processes heat, ionize and metal-enrich the gas, thus
altering the initial conditions for the next generation of star formation.
Stars formed from gas that has been altered significantly by radiative and/or
mechanical feedback, but not by metal enrichment (Pop III.2) are expected to
have significantly smaller masses than Pop III.1 stars because of more
efficient cooling from enhanced HD production. Stars formed from gas that is
metal-enriched to levels that affect the dynamics of the collapse (the first
Pop II stars) are also expected to have relatively low masses. We briefly
compare the above star formation scenarios to what is known about present-day
star formation.Comment: 16 pages, including 11 figures, Review paper to appear in "First
Stars III", eds. B. O'Shea, A. Heger and T. Abe
Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
We study non-asymptotic fundamental limits for transmitting classical
information over memoryless quantum channels, i.e. we investigate the amount of
classical information that can be transmitted when a quantum channel is used a
finite number of times and a fixed, non-vanishing average error is permissible.
We consider the classical capacity of quantum channels that are image-additive,
including all classical to quantum channels, as well as the product state
capacity of arbitrary quantum channels. In both cases we show that the
non-asymptotic fundamental limit admits a second-order approximation that
illustrates the speed at which the rate of optimal codes converges to the
Holevo capacity as the blocklength tends to infinity. The behavior is governed
by a new channel parameter, called channel dispersion, for which we provide a
geometrical interpretation.Comment: v2: main results significantly generalized and improved; v3: extended
to image-additive channels, change of title, journal versio
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