  The distributed source coding problem is considered when the sensors, or
encoders, are under Byzantine attack; that is, an unknown number of sensors
have been reprogrammed by a malicious intruder to undermine the reconstruction
at the fusion center. Three different forms of the problem are considered. The
first is a variable-rate setup, in which the decoder adaptively chooses the
rates at which the sensors transmit. An explicit characterization of the
variable-rate minimum achievable sum rate is stated, given by the maximum
entropy over the set of distributions indistinguishable from the true source
distribution by the decoder. In addition, two forms of the fixed-rate problem
are considered, one with deterministic coding and one with randomized coding.
The achievable rate regions are given for both these problems, with a larger
region achievable using randomized coding, though both are suboptimal compared
to variable-rate coding.
