Nonlinear network coding is necessary to combat General Byzantine attacks

We consider the problem of achieving capacity through network coding when some of the nodes act covertly as Byzantine adversaries. For several case-study networks, we investigate rates of reliable communication through network coding and upper bounds on capacity. We show that linear codes are inadequate in general, and a slight augmentation of the class of linear codes can increase throughput. Furthermore, we show that even this nonlinear augmentation may not be enough to achieve capacity. We introduce a new class of codes known as bounded-linear that make use of distributions defined over bounded sets of integers subject to linear constraints using real arithmetic.