659 research outputs found
One-shot lossy quantum data compression
We provide a framework for one-shot quantum rate distortion coding, in which
the goal is to determine the minimum number of qubits required to compress
quantum information as a function of the probability that the distortion
incurred upon decompression exceeds some specified level. We obtain a one-shot
characterization of the minimum qubit compression size for an
entanglement-assisted quantum rate-distortion code in terms of the smooth
max-information, a quantity previously employed in the one-shot quantum reverse
Shannon theorem. Next, we show how this characterization converges to the known
expression for the entanglement-assisted quantum rate distortion function for
asymptotically many copies of a memoryless quantum information source. Finally,
we give a tight, finite blocklength characterization for the
entanglement-assisted minimum qubit compression size of a memoryless isotropic
qubit source subject to an average symbol-wise distortion constraint.Comment: 36 page
The Likelihood Encoder for Lossy Compression
A likelihood encoder is studied in the context of lossy source compression.
The analysis of the likelihood encoder is based on the soft-covering lemma. It
is demonstrated that the use of a likelihood encoder together with the
soft-covering lemma yields simple achievability proofs for classical source
coding problems. The cases of the point-to-point rate-distortion function, the
rate-distortion function with side information at the decoder (i.e. the
Wyner-Ziv problem), and the multi-terminal source coding inner bound (i.e. the
Berger-Tung problem) are examined in this paper. Furthermore, a non-asymptotic
analysis is used for the point-to-point case to examine the upper bound on the
excess distortion provided by this method. The likelihood encoder is also
related to a recent alternative technique using properties of random binning
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
Consciousness, cognition, and the hierarchy of context: extending the global neuronal workspace model
We adapt an information theory analysis of interacting cognitive biological and social modules to the problem of the global neuronal workspace, the new standard neuroscience paradigm for consciousness. Tunable punctuation emerges in a natural way, suggesting the possibility of fitting appropriate phase transition power law, and away from transition, generalized Onsager relation expressions, to observational data on conscious reaction. The development can be extended in a straightforward manner to include psychosocial stress, culture, or other cognitive modules which constitute a structured, embedding hierarchy of contextual constraints acting at a slower rate than neuronal function itself. This produces a 'biopsychosociocultural' model of individual consciousness that, while otherwise quite close to the standard treatment, meets compelling philosophical and other objections to brain-only descriptions
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