On random network coding based information dissemination

We study the gains to be had by using random linear coding (RLC) for simultaneously disseminating k distinct messages in a network of n nodes in a decentralized and distributed manner for arbitrary k and n. The goal is to rapidly disseminate all the messages among all the nodes. Any node can communicate with any of the other nodes but only one at a time, nodes only have knowledge about their own contents, and the bandwidth for every transmission between two nodes is limited (does not scale with k or n). An efficient and well-studied protocol for message dissemination in such a framework is randomized gossip based message dissemination. The problem has been studied extensively without using any coding for message dissemination. We show using analysis and simulation that, in the regime k ges (ln(n))
³
, RLC based dissemination reduces the dissemination time (the time-steps to disseminate all the messages among all the nodes) by a factor of otimes(ln(n)) as compared to disseminating the messages sequentially (i.e., one after the other) as implicit in most non-coding based technique. In the regime k les (ln(n))
²
, the dissemination time with RLC goes down by a factor of Omega(radick / ln k). More precisely, our results indicate that a RLC based protocol disseminates all the messages among all the nodes in time ck + O(radick ln(k)(ln(n)) for a suitable constant c > 0. Analytical results show that, c < 3.46 using pull based dissemination, and c < 5.96 using push based dissemination, but reported simulations suggest c < 2 might be a tighter bound