Iterative Source-Channel Coding Approach to Witsenhausen's   Counterexample
  In 1968, Witsenhausen introduced his famous counterexample where he showed that even in the simple linear quadratic static team decision problem, complex nonlinear decisions could outperform any given linear decision. This problem has served as a benchmark problem for decades where researchers try to achieve the optimal solution. This paper introduces a systematic iterative source--channel coding approach to solve problems of the Witsenhausen Counterexample-character. The advantage of the presented approach is its simplicity. Also, no assumptions are made about the shape of the space of policies. The minimal cost obtained using the introduced method is 0.16692462, which is the lowest known to date. 
Johannes Kron, Ather Gattami, Tobias J. Oechtering, Mikael Skoglund
math.OC