Graph Entropy, Network Coding and Guessing games

We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below with the number of vertices minus the size of the graph’s shortest index code. We show that the Network Coding solvability of each specific multiple unicast network is completely determined by the entropy (as well as by the shortest index code) of the directed graph that occur by identifying each source node with each corresponding target node. Shannon’s information inequalities can be used to calculate upper bounds on a graph’s entropy as well as calculating the size of the minimal index code. Recently, a number of new families of so-called non-shannon-type information inequalities have been discovered. It has been shown that there exist communication networks with a capacity strictly ess than required for solvability, but where this fact can...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Søren Riis
• Keywords: CORR 2007, Directed Graph, Education, Entropy, Information Inequalities