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

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

We take a new look at the issue of network capacity. It is shown that network coding is an essential ingredient in achieving the capacity of a network. Building on recent work by Li et al.(see Proc. 2001 IEEE Int. Symp. Information Theory, p.102), who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary networks and robust networking. For networks which are restricted to using linear network codes, we find necessary and sufficient conditions for the feasibility of any given set of connections over a given network. We also consider the problem of network recovery for nonergodic link failures. For the multicast setup we prove that there exist coding strategies that provide maximally robust networks and that do not require adaptation of the network interior to the failure pattern in question. The results are derived for both delay-free networks and networks with delays.

/pdf/an-algebraic-approach-to-network-coding-15ubrgla2l.pdf

An algebraic approach to 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

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 for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory.

/pdf/network-coding-theory-single-sources-yhopi34qlc.pdf

Network coding theory: single sources

We apply the concept of stopping times of martingales to problems in classical probability theory regarding the occurrence of sequence patterns in repeated experiments. For every finite collection of sequences of possible outcomes, we compute the expected waiting time till one of them is observed in a run of experiments. Also we compute the probability for each sequence to be the first to appear. The main result, with a transparent proof, is a generalization of some well-known facts on Bernoulli process including formulas of Feller and the "leading number" algorithm of Conway.

/pdf/a-martingale-approach-to-the-study-of-occurrence-of-sequence-1e24vl9bz7.pdf

Shuo-Yen Robert Li

Papers

Network information flow

Linear network coding

Network Coding Theory

Network coding theory: single sources

A Martingale Approach to the Study of Occurrence of Sequence Patterns in Repeated Experiments