Distributed information-theoretic biclustering of two memoryless sources

A novel multi-terminal source coding problem motivated by biclustering applications is investigated. In this setting, two separate encoders observe two dependent memoryless processes Xⁿ and Zⁿ, respectively. The encoders' goal is to find rate-limited functions f(Xⁿ) and g(Zⁿ) that maximize asymptotically the mutual information I(f(Xⁿ); g(Zⁿ)) ≥ nμ. We derive non-trivial inner and outer bounds on the optimal characterization of the achievable rates for this problem. Applications also arise in the context of distributed hypothesis testing against independence under communication constraints.