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

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

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

We present a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks. Network nodes independently and randomly select linear mappings from inputs onto output links over some field. We show that this achieves capacity with probability exponentially approaching 1 with the code length. We also demonstrate that random linear coding performs compression when necessary in a network, generalizing error exponents for linear Slepian-Wolf coding in a natural way. Benefits of this approach are decentralized operation and robustness to network changes or link failures. We show that this approach can take advantage of redundant network capacity for improved success probability and robustness. We illustrate some potential advantages of random linear network coding over routing in two examples of practical scenarios: distributed network operation and networks with dynamically varying connections. Our derivation of these results also yields a new bound on required field size for centralized network coding on general multicast networks

/pdf/a-random-linear-network-coding-approach-to-multicast-4j4cdceo1m.pdf

A Random Linear Network Coding Approach to Multicast

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

Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm f...

/pdf/network-coding-theory-36ca8j6gow.pdf

Network Coding Theory

Error correction in existing point-to-point communication networks is done on a link-by-link basis, which is referred to in this paper as classical error correction. Inspired by network coding, we introduce in this two-part paper a new paradigm called network error correction .T he theory thus developed subsumes classical algebraic coding theory as a special case. In Part I, we discuss the basic concepts and prove the network generalizations of the Hamming bound and the Singleton bound in classical algebraic coding theory. By studying a few elementary examples, the relation between network error correction and classical error correction is investigated.

/pdf/network-error-correction-i-basic-concepts-and-upper-bounds-3dd4slgb7h.pdf

Ning Cai

Papers

Network information flow

Linear network coding

Secure network coding

Network Coding Theory

Network Error Correction, I: Basic Concepts and Upper Bounds