The Corruption Bound, Log Rank, and Communication Complexity
  We prove upper bounds on deterministic communication complexity in terms of log of the rank and simple versions of the corruption bound.   Our bounds are a simplified version of the results of Gavinsky and Lovett, using the same set of tools. We also give an elementary proof for the upper bound on communication complexity in terms of rank proved by Lovett. 
Adi Shraibman
cs.CC