2,393 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
Coalitional Games for Transmitter Cooperation in MIMO Multiple Access Channels
Cooperation between nodes sharing a wireless channel is becoming increasingly
necessary to achieve performance goals in a wireless network. The problem of
determining the feasibility and stability of cooperation between rational nodes
in a wireless network is of great importance in understanding cooperative
behavior. This paper addresses the stability of the grand coalition of
transmitters signaling over a multiple access channel using the framework of
cooperative game theory. The external interference experienced by each TX is
represented accurately by modeling the cooperation game between the TXs in
\emph{partition form}. Single user decoding and successive interference
cancelling strategies are examined at the receiver. In the absence of
coordination costs, the grand coalition is shown to be \emph{sum-rate optimal}
for both strategies. Transmitter cooperation is \emph{stable}, if and only if
the core of the game (the set of all divisions of grand coalition utility such
that no coalition deviates) is nonempty. Determining the stability of
cooperation is a co-NP-complete problem in general. For a single user decoding
receiver, transmitter cooperation is shown to be \emph{stable} at both high and
low SNRs, while for an interference cancelling receiver with a fixed decoding
order, cooperation is stable only at low SNRs and unstable at high SNR. When
time sharing is allowed between decoding orders, it is shown using an
approximate lower bound to the utility function that TX cooperation is also
stable at high SNRs. Thus, this paper demonstrates that ideal zero cost TX
cooperation over a MAC is stable and improves achievable rates for each
individual user.Comment: in review for publication in IEEE Transactions on Signal Processin
Gaussian Multiple Access via Compute-and-Forward
Lattice codes used under the Compute-and-Forward paradigm suggest an
alternative strategy for the standard Gaussian multiple-access channel (MAC):
The receiver successively decodes integer linear combinations of the messages
until it can invert and recover all messages. In this paper, a multiple-access
technique called CFMA (Compute-Forward Multiple Access) is proposed and
analyzed. For the two-user MAC, it is shown that without time-sharing, the
entire capacity region can be attained using CFMA with a single-user decoder as
soon as the signal-to-noise ratios are above . A partial analysis
is given for more than two users. Lastly the strategy is extended to the
so-called dirty MAC where two interfering signals are known non-causally to the
two transmitters in a distributed fashion. Our scheme extends the previously
known results and gives new achievable rate regions.Comment: to appear in IEEE Transactions on Information Theor
Lecture Notes on Network Information Theory
These lecture notes have been converted to a book titled Network Information
Theory published recently by Cambridge University Press. This book provides a
significantly expanded exposition of the material in the lecture notes as well
as problems and bibliographic notes at the end of each chapter. The authors are
currently preparing a set of slides based on the book that will be posted in
the second half of 2012. More information about the book can be found at
http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of
the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/
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