There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Wireless Communications

We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be multicast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. We study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the max-flow min-cut theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.

http://www.inf.fu-berlin.de/lehre/WS11/Wireless/papers/CodAhlswede00.pdf

Network information flow

Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

/pdf/information-theory-inference-and-learning-algorithms-gbv6i2zu22.pdf

Information Theory, Inference and Learning Algorithms

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Consider a communication network in which certain source nodes multicast information to other nodes on the network in the multihop fashion where every node can pass on any of its received data to others. We are interested in how fast each node can receive the complete information, or equivalently, what the information rate arriving at each node is. Allowing a node to encode its received data before passing it on, the question involves optimization of the multicast mechanisms at the nodes. Among the simplest coding schemes is linear coding, which regards a block of data as a vector over a certain base field and allows a node to apply a linear transformation to a vector before passing it on. We formulate this multicast problem and prove that linear coding suffices to achieve the optimum, which is the max-flow from the source to each receiving node.

/pdf/linear-network-coding-4y41qrgncb.pdf

Linear network coding

This book contains a thorough discussion of the classical topics in information theory together with the first comprehensive treatment of network coding, a subject first emerged under information theory in the mid 1990's that has now diffused into coding theory, computer networks, wireless communications, complexity theory, cryptography, graph theory, etc. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.

Information Theory and Network Coding

Recent work on network coding renders a new view on multicasting in a network In the paradigm of network coding, the nodes in a network are allowed to encode the information received from the input links The usual function of switching at a node is a special case of network coding The advantage of network coding is that the full capacity of the network can be utilized In this paper, we propose a new model which incorporates network coding and information security Specifically, a collection of subsets of links is given, and a wiretapper is allowed to access any one (but not more than one) of these subsets without being able to obtain any information about the message transmitted Our model includes secret sharing as a special case We present a construction of secure linear network codes provided a certain graph-theoretic sufficient condition is satisfied

Secure network coding

This book provides an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.

/pdf/a-first-course-in-information-theory-y7j55kfjxd.pdf

Raymond W. Yeung

Papers

Network information flow

Linear network coding

Information Theory and Network Coding

Secure network coding

A First Course in Information Theory