Information dissemination in networks via linear iterative strategies over finite fields

— Given an arbitrary network of interconnected nodes, each with an initial value from a discrete set, we consider the problem of distributively disseminating these initial values under the constraint that the nodes can only process and communicate values in that set. To solve this problem, we treat the initial values as elements in a finite field and employ a linear iterative strategy, whereby at each time-step, each node in the network transmits a value that is a linear combination of its own value and the most recent transmissions of its neighbors. Our approach is an important (and non-trivial) extension of previous work on linear iterative strategies with real-valued transmissions and operations, and can find applications in networks that have communication or computational constraints. We show that if the weights for the linear iteration are chosen randomly (uniformly and independently) from a finite field of sufficiently large size, then with some nonzero probability, any ...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Shreyas Sundaram, Christoforos N. Hadjicostis
• Keywords: CDC 2009, Control Systems, Initial Value, Linear, finite fields