31,694 research outputs found
Generalizations of Fano's Inequality for Conditional Information Measures via Majorization Theory
Fano's inequality is one of the most elementary, ubiquitous, and important
tools in information theory. Using majorization theory, Fano's inequality is
generalized to a broad class of information measures, which contains those of
Shannon and R\'{e}nyi. When specialized to these measures, it recovers and
generalizes the classical inequalities. Key to the derivation is the
construction of an appropriate conditional distribution inducing a desired
marginal distribution on a countably infinite alphabet. The construction is
based on the infinite-dimensional version of Birkhoff's theorem proven by
R\'{e}v\'{e}sz [Acta Math. Hungar. 1962, 3, 188{\textendash}198], and the
constraint of maintaining a desired marginal distribution is similar to
coupling in probability theory. Using our Fano-type inequalities for Shannon's
and R\'{e}nyi's information measures, we also investigate the asymptotic
behavior of the sequence of Shannon's and R\'{e}nyi's equivocations when the
error probabilities vanish. This asymptotic behavior provides a novel
characterization of the asymptotic equipartition property (AEP) via Fano's
inequality.Comment: 44 pages, 3 figure
A Rank-Metric Approach to Error Control in Random Network Coding
The problem of error control in random linear network coding is addressed
from a matrix perspective that is closely related to the subspace perspective
of K\"otter and Kschischang. A large class of constant-dimension subspace codes
is investigated. It is shown that codes in this class can be easily constructed
from rank-metric codes, while preserving their distance properties. Moreover,
it is shown that minimum distance decoding of such subspace codes can be
reformulated as a generalized decoding problem for rank-metric codes where
partial information about the error is available. This partial information may
be in the form of erasures (knowledge of an error location but not its value)
and deviations (knowledge of an error value but not its location). Taking
erasures and deviations into account (when they occur) strictly increases the
error correction capability of a code: if erasures and
deviations occur, then errors of rank can always be corrected provided that
, where is the minimum rank distance of the
code. For Gabidulin codes, an important family of maximum rank distance codes,
an efficient decoding algorithm is proposed that can properly exploit erasures
and deviations. In a network coding application where packets of length
over are transmitted, the complexity of the decoding algorithm is given
by operations in an extension field .Comment: Minor corrections; 42 pages, to be published at the IEEE Transactions
on Information Theor
Noise adaptive training for subspace Gaussian mixture models
Noise adaptive training (NAT) is an effective approach to normalise the environmental distortions in the training data. This paper investigates the model-based NAT scheme using joint uncertainty decoding (JUD) for subspace Gaussian mixture models (SGMMs). A typical SGMM acoustic model has much larger number of surface Gaussian components, which makes it computationally infeasible to compensate each Gaussian explicitly. JUD tackles the problem by sharing the compensation parameters among the Gaussians and hence reduces the computational and memory demands. For noise adaptive training, JUD is reformulated into a generative model, which leads to an efficient expectation-maximisation (EM) based algorithm to update the SGMM acoustic model parameters. We evaluated the SGMMs with NAT on the Aurora 4 database, and obtained higher recognition accuracy compared to systems without adaptive training. Index Terms: adaptive training, noise robustness, joint uncertainty decoding, subspace Gaussian mixture model
A hypothesis testing approach for communication over entanglement assisted compound quantum channel
We study the problem of communication over a compound quantum channel in the
presence of entanglement. Classically such channels are modeled as a collection
of conditional probability distributions wherein neither the sender nor the
receiver is aware of the channel being used for transmission, except for the
fact that it belongs to this collection. We provide near optimal achievability
and converse bounds for this problem in the one-shot quantum setting in terms
of quantum hypothesis testing divergence. We also consider the case of informed
sender, showing a one-shot achievability result that converges appropriately in
the asymptotic and i.i.d. setting. Our achievability proof is similar in spirit
to its classical counterpart. To arrive at our result, we use the technique of
position-based decoding along with a new approach for constructing a union of
two projectors, which can be of independent interest. We give another
application of the union of projectors to the problem of testing composite
quantum hypotheses.Comment: 21 pages, version 3. Added an application to the composite quantum
hypothesis testing. Expanded introductio
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