This article surveys all known fields of network coding theory and leads the reader through
the antecedents of the network coding theory to the most recent results, considering also …

We show that the network coding and index coding problems are equivalent. This
equivalence holds in the general setting which includes linear and nonlinear codes …

A sender holds a word x consisting of n blocks xi, each of t bits, and wishes to broadcast a
codeword to m receivers, R 1,..., R m. Each receiver R i is interested in one block, and has …

Private information retrieval (PIR) is the problem of retrieving one message out of K
messages from N noncommunicating replicated databases, where each database stores all …

Index coding is a canonical problem in network information theory that studies the
fundamental limit and optimal coding schemes for broadcasting multiple messages to …

A marginal problem asks whether a given family of marginal distributions for some set of
random variables arises from some joint distribution of these variables. Here, we point out …

In this tutorial paper, we focus on the basic theory of linear secure network coding. Our goal
is to present fundamental results and provide preliminary knowledge for anyone interested …

This work addresses the computational complexity of achieving the capacity of a general
network coding instance. It has been shown [Lehman and Lehman, SODA 2005] that …

Index Coding has received considerable attention recently motivated in part by real-world
applications and in part by its connection to Network Coding. The basic setting of Index …

We resolve three long-standing open problems, namely the (algorithmic) decidability of
network coding, the decidability of conditional information inequalities, and the decidability …