On delay and security in network coding

Abstract

In this thesis, delay and security issues in network coding are considered. First, we study the delay incurred in the transmission of a fixed number of packets through acyclic networks comprised of erasure links. The two transmission schemes studied are routing with hop-by-hop retransmissions, where every node in the network simply stores and forwards its received packets, and linear coding, where nodes mix their packets by forwarding linear combinations of all their previously received packets. We show that even though the achievable rates of coding and routing are the same, network coding can have an increasingly better performance than routing as the number of packets increases. Secondly, we investigate the security benefits of network coding. We investigate the achievable secrecy rate region in a general network of noisy wiretap channels with general communication demands. The eavesdropper has access to an unknown set of links, and on the wiretapped links observes a degraded version of the intended receiver's observation. While characterizing the capacity in general is an open problem, in the noise-free case there exist inner and outer bounds. In the noisy case, we show how one can change any of the wiretap channels to a noiseless degraded broadcast channel, so that the derived network's rate region bounds, and under certain conditions is equivalent, to that of the initial network. Specifically, we showed that in case the eavesdropper can choose only a single link to wiretap at each time, then one can change all the links in the network with corresponding noiseless ones, creating an equivalent noiseless secrecy problem. In the case where the eavesdropper can wiretap multiple links simultaneously, we derive upper and lower bounding noiseless network problems. Finally, we consider design practical code design for the detection of adversarial errors in a distributed storage system. We build on work of functions that can fool linear polynomials to create and communicate hash functions of the data in order to detect with high probability the maliciously attacked nodes in the system.