  We study the problem of distributed information bottleneck, in which multiple
encoders separately compress their observations in a manner such that,
collectively, the compressed signals preserve as much information as possible
about another signal. The model generalizes Tishby's centralized information
bottleneck method to the setting of multiple distributed encoders. We establish
single-letter characterizations of the information-rate region of this problem
for both i) a class of discrete memoryless sources and ii) memoryless vector
Gaussian sources. Furthermore, assuming a sum constraint on rate or complexity,
for both models we develop Blahut-Arimoto type iterative algorithms that allow
to compute optimal information-rate trade-offs, by iterating over a set of
self-consistent equations.
