Insights into Network Coding Using Tools From Linear Algebra and Matroid Theory

Abstract

Traditionally, the transmission of information through a network was carried out using store-and-forward techniques. This entails managing information bits in a network analogous to commodity flow, without mixing or combining them. Network Coding is the paradigm of information flow where coding at the intermediate nodes could achieve a network capacity that surpassed what could be achieved by routing. Index Coding can be perceived as a degenerate case of network coding where the network has a single link of finite capacity and all other infinite capacity links. The thesis addresses these topics under different sub-heads as follows:

• Binary multicast networks and their solvability over higher finite fields • Minrank of unicast-uniprior index coding problems • Scalar Linear Codes for neighboring interference problem • Optimized Instantly Decodable Network Codes • The number of optimal index codes