Design and Analysis of Network Codes

Citation

Jaggi, Sidharth (2006) Design and Analysis of Network Codes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7ERZ-H253. https://resolver.caltech.edu/CaltechETD:etd-05302006-131149

Abstract

The information theoretic aspects of large networks with many terminals present several interesting and non-intuitive phenomena. One such crucial phenomenon was first explored in a detailed manner in the excellent work by Ahlswede at al. It compared two paradigms for operating a network -- one in which interior nodes were restricted to only copying and forwarding incoming messages on outgoing links, and another in which internal nodes were allowed to perform non-trivial arithmetic operations on information on incoming links to generate information on outgoing links. It showed that the latter approach could substantially improve throughput compared to the more traditional scenario. Further work by various authors showed how to design codes (called network codes) to transmit under this new paradigm and also demonstrated exciting new phenomena for these codes such as robustness against network failures, distributed design, and increased security.

In this work, we consider the low-complexity design and analysis of network codes, with a focus on codes for multicasting information. We examine both centralized and decentralized design of such codes, and also both randomized and deterministic design algorithms. We compare different notions of linearity and show the interplay between these notions in the design of linear network codes. We determine bounds on the complexity of network codes. We also consider the problem of error-correction and secrecy for network codes when a malicious adversary controls some subset of the network resources.

Thesis Files