21,664 research outputs found
The AWGN Red Alert Problem
Consider the following unequal error protection scenario. One special
message, dubbed the "red alert" message, is required to have an extremely small
probability of missed detection. The remainder of the messages must keep their
average probability of error and probability of false alarm below a certain
threshold. The goal then is to design a codebook that maximizes the error
exponent of the red alert message while ensuring that the average probability
of error and probability of false alarm go to zero as the blocklength goes to
infinity. This red alert exponent has previously been characterized for
discrete memoryless channels. This paper completely characterizes the optimal
red alert exponent for additive white Gaussian noise channels with block power
constraints.Comment: 13 pages, 10 figures, To appear in IEEE Transactions on Information
Theor
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
Distributed Hypothesis Testing Over Multi-Access Channels
International audienceConsider distributed hypothesis testing over multiple-access channels (MACs), where the receiver wishes to maximize the type-II error exponent under a constrained type-I error probability. For this setup, we propose a scheme that combines hybrid coding with a MAC-version of Borades unequal error protection. It achieves the optimal type-II error exponent for a generalization of testing against independence over an orthogonal MAC when the transmitters' sources are independent. In this case, hybrid coding can be replaced by the simpler separate source-channel coding. The paper also presents upper and lower bounds on the optimal type-II error exponent for generalized testing against independence of Gaussian sources over a Gaussian MAC. The bounds are close and significantly larger than a type-II error exponent that is achievable using separate source-channel coding
Exponent Trade-off for Hypothesis Testing Over Noisy Channels
International audienceThe distributed hypothesis testing (DHT) problem is considered, in which the joint distribution of a pair of sequences present at separated terminals, is governed by one of two possible hypotheses. The decision needs to be made by one of the terminals (the "decoder"). The other terminal (the "encoder") uses a noisy channel in order to help the decoder with the decision. This problem can be seen as a generalization of the side-information variant of the DHT problem, where the rate-limited link is replaced by a noisy channel. A recent work by Salehkalaibar and Wigger has derived an achievable Stein exponent for this problem, by employing concepts from the DHT scheme of Shimokawa et al., and from unequal error protection coding for a single special message. In this work we extend the view to a trade-off between the two error exponents, additionally building on multiple codebooks and two special messages with unequal error protection. As a by product, we also present an achievable exponent trade-off for a rate-limited link, which generalizes Shimokawa et al.
Cross-National Differences in Victimization : Disentangling the Impact of Composition and Context
Varying rates of criminal victimization across countries are assumed to be the outcome of countrylevel structural constraints that determine the supply ofmotivated o¡enders, as well as the differential composition within countries of suitable targets and capable guardianship. However, previous empirical tests of these ‘compositional’ and ‘contextual’ explanations of cross-national di¡erences
have been performed upon macro-level crime data due to the unavailability of comparable individual-level data across countries. This limitation has had two important consequences for cross-national crime research. First, micro-/meso-level mechanisms underlying cross-national differences cannot be truly inferred from macro-level data. Secondly, the e¡ects of contextual measures (e.g. income inequality) on crime are uncontrolled for compositional heterogeneity. In this
paper, these limitations are overcome by analysing individual-level victimization data across 18 countries from the International CrimeVictims Survey. Results from multi-level analyses on theft and violent victimization indicate that the national level of income inequality is positively related to risk, independent of compositional (i.e. micro- and meso-level) di¡erences. Furthermore, crossnational variation in victimization rates is not only shaped by di¡erences in national context, but
also by varying composition. More speci¢cally, countries had higher crime rates the more they consisted of urban residents and regions with lowaverage social cohesion.
Diversité ethno-culturelle et différentiel de pauvreté multidimensionnelle au Cameroun
Peu de recherches ont concilié le caractère multidimensionnel de la pauvreté avec le conditionnement culturel des populations pour orienter les politiques. La démarche de la MES (Modélisation en Équations Structurelles) à travers sa technique de comparaison de modèles nichés a permis de formuler et de tester les hypothèses de recherche. Les résultats montrent que les différences de niveau observées sur les dimensions de pauvreté résultent significativement (ce qui ne veut pas dire exclusivement) des systèmes de valeurs culturelles partagés au sein des groupes. Les facteurs par lesquels transite l'élément culturel vers le domaine de la pauvreté sont de deux ordres. Il s'agit du différentiel des perceptions et des déterminants de la pauvreté. Compte tenu de ces résultats et pour une stratégie crédible de réduction de la pauvreté, nous proposons une approche participative et décentralisée prudente pour définir les actions de lutte répondant aux besoins exprimés par les populations concernées.Pauvreté multidimensionnelle, culture, différentiel de pauvreté, MES, modèles nichés, variables latentes, indicateurs de pauvreté
Distributed Hypothesis Testing over a Noisy Channel: Error-exponents Trade-off
A two-terminal distributed binary hypothesis testing (HT) problem over a
noisy channel is studied. The two terminals, called the observer and the
decision maker, each has access to independent and identically distributed
samples, denoted by and , respectively. The observer
communicates to the decision maker over a discrete memoryless channel (DMC),
and the decision maker performs a binary hypothesis test on the joint
probability distribution of based on and
the noisy information received from the observer. The trade-off between the
exponents of the type I and type II error probabilities in HT is investigated.
Two inner bounds are obtained, one using a separation-based scheme that
involves type-based compression and unequal error-protection channel coding,
and the other using a joint scheme that incorporates type-based hybrid coding.
The separation-based scheme is shown to recover the inner bound obtained by Han
and Kobayashi for the special case of a rate-limited noiseless channel, and
also the one obtained by the authors previously for a corner point of the
trade-off. Exact single-letter characterization of the optimal trade-off is
established for the special case of testing for the marginal distribution of
, when is unavailable. Our results imply that a
separation holds in this case, in the sense that the optimal trade-off is
achieved by a scheme that performs independent HT and channel coding. Finally,
we show via an example that the joint scheme achieves a strictly tighter bound
than the separation-based scheme for some points of the error-exponent
trade-off
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