Design and analysis of network codes
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 [1]. 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 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 properties of these codes such as distributed design, increased security, and robustness against network failures.
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 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…
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