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. newline