1,323 research outputs found
Brascamp-Lieb Inequality and Its Reverse: An Information Theoretic View
We generalize a result by Carlen and Cordero-Erausquin on the equivalence
between the Brascamp-Lieb inequality and the subadditivity of relative entropy
by allowing for random transformations (a broadcast channel). This leads to a
unified perspective on several functional inequalities that have been gaining
popularity in the context of proving impossibility results. We demonstrate that
the information theoretic dual of the Brascamp-Lieb inequality is a convenient
setting for proving properties such as data processing, tensorization,
convexity and Gaussian optimality. Consequences of the latter include an
extension of the Brascamp-Lieb inequality allowing for Gaussian random
transformations, the determination of the multivariate Wyner common information
for Gaussian sources, and a multivariate version of Nelson's hypercontractivity
theorem. Finally we present an information theoretic characterization of a
reverse Brascamp-Lieb inequality involving a random transformation (a multiple
access channel).Comment: 5 pages; to be presented at ISIT 201
Capacity of wireless erasure networks
In this paper, a special class of wireless networks, called wireless erasure networks, is considered. In these networks, each node is connected to a set of nodes by possibly correlated erasure channels. The network model incorporates the broadcast nature of the wireless environment by requiring each node to send the same signal on all outgoing channels. However, we assume there is no interference in reception. Such models are therefore appropriate for wireless networks where all information transmission is packetized and where some mechanism for interference avoidance is already built in. This paper looks at multicast problems over these networks. The capacity under the assumption that erasure locations on all the links of the network are provided to the destinations is obtained. It turns out that the capacity region has a nice max-flow min-cut interpretation. The definition of cut-capacity in these networks incorporates the broadcast property of the wireless medium. It is further shown that linear coding at nodes in the network suffices to achieve the capacity region. Finally, the performance of different coding schemes in these networks when no side information is available to the destinations is analyzed
Channel Coding at Low Capacity
Low-capacity scenarios have become increasingly important in the technology
of the Internet of Things (IoT) and the next generation of mobile networks.
Such scenarios require efficient and reliable transmission of information over
channels with an extremely small capacity. Within these constraints, the
performance of state-of-the-art coding techniques is far from optimal in terms
of either rate or complexity. Moreover, the current non-asymptotic laws of
optimal channel coding provide inaccurate predictions for coding in the
low-capacity regime. In this paper, we provide the first comprehensive study of
channel coding in the low-capacity regime. We will investigate the fundamental
non-asymptotic limits for channel coding as well as challenges that must be
overcome for efficient code design in low-capacity scenarios.Comment: 39 pages, 5 figure
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
Cooperative Strategies for Simultaneous and Broadcast Relay Channels
Consider the \emph{simultaneous relay channel} (SRC) which consists of a set
of relay channels where the source wishes to transmit common and private
information to each of the destinations. This problem is recognized as being
equivalent to that of sending common and private information to several
destinations in presence of helper relays where each channel outcome becomes a
branch of the \emph{broadcast relay channel} (BRC). Cooperative schemes and
capacity region for a set with two memoryless relay channels are investigated.
The proposed coding schemes, based on \emph{Decode-and-Forward} (DF) and
\emph{Compress-and-Forward} (CF) must be capable of transmitting information
simultaneously to all destinations in such set.
Depending on the quality of source-to-relay and relay-to-destination
channels, inner bounds on the capacity of the general BRC are derived. Three
cases of particular interest are considered: cooperation is based on DF
strategy for both users --referred to as DF-DF region--, cooperation is based
on CF strategy for both users --referred to as CF-CF region--, and cooperation
is based on DF strategy for one destination and CF for the other --referred to
as DF-CF region--. These results can be seen as a generalization and hence
unification of previous works. An outer-bound on the capacity of the general
BRC is also derived. Capacity results are obtained for the specific cases of
semi-degraded and degraded Gaussian simultaneous relay channels. Rates are
evaluated for Gaussian models where the source must guarantee a minimum amount
of information to both users while additional information is sent to each of
them.Comment: 32 pages, 7 figures, To appear in IEEE Trans. on Information Theor
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