  Three decades of research in communication complexity have led to the
invention of a number of techniques to lower bound randomized communication
complexity. The majority of these techniques involve properties of large
submatrices (rectangles) of the truth-table matrix defining a communication
problem. The only technique that does not quite fit is information complexity,
which has been investigated over the last decade. Here, we connect information
complexity to one of the most powerful "rectangular" techniques: the
recently-introduced smooth corruption (or "smooth rectangle") bound. We show
that the former subsumes the latter under rectangular input distributions. We
conjecture that this subsumption holds more generally, under arbitrary
distributions, which would resolve the long-standing direct sum question for
randomized communication. As an application, we obtain an optimal $\Omega(n)$
lower bound on the information complexity---under the {\em uniform
distribution}---of the so-called orthogonality problem (ORT), which is in turn
closely related to the much-studied Gap-Hamming-Distance (GHD). The proof of
this bound is along the lines of recent communication lower bounds for GHD, but
we encounter a surprising amount of additional technical detail.
