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

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 $\epsilon\in(0,1)$ 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 $\epsilon$, 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