  In this paper, we propose a scheme, called the "algebraic watchdog" for
wireless network coding, in which nodes can detect malicious behaviors
probabilistically, police their downstream neighbors locally using overheard
messages, and, thus, provide a secure global "self-checking network". Unlike
traditional Byzantine detection protocols which are receiver-based, this
protocol gives the senders an active role in checking the node downstream. This
work is inspired by Marti et. al.'s watchdog-pathrater, which attempts to
detect and mitigate the effects of routing misbehavior.
  As the first building block of a such system, we focus on a two-hop network.
We present a graphical model to understand the inference process nodes execute
to police their downstream neighbors; as well as to compute, analyze, and
approximate the probabilities of misdetection and false detection. In addition,
we present an algebraic analysis of the performance using an hypothesis testing
framework, that provides exact formulae for probabilities of false detection
and misdetection.
