A multi-hop multi-source Algebraic Watchdog

In our previous work (`An Algebraic Watchdog for Wireless Network Coding´), we proposed a new scheme in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages; thus, provide a secure global self-checking network. As the first building block of such a system, we focused on a two-hop network, and presented a graphical model to understand the inference process by which nodes police their downstream neighbors and to compute the probabilities of misdetection and false detection. In this paper, we extend the Algebraic Watchdog to a more general network setting, and propose a protocol in which we can establish trust in coded systems in a distributed manner. We develop a graphical model to detect the presence of an adversarial node downstream within a general two-hop network. The structure of the graphical model (a trellis) lends itself to well-known algorithms, such as Viterbi algorithm, that can compute the probabilities of misdetection and false detection. Using this as a building block, we generalize our scheme to multi-hop networks. We show analytically that as long as the min-cut is not dominated by the Byzantine adversaries, upstream nodes can monitor downstream neighbors and allow reliable communication with certain probability. Finally, we present preliminary simulation results that support our analysis.