On interactive communication

Ahlswede has previously introduced an abstract correlated source (𝒱×𝒲,S) with outputs (υ, ω)∈S⊂𝒱×𝒲, where persons P_𝒱 and P_𝒲 observe υ and ω, respectively. More recently, Orlitsky considered the minimal number C _m of bits to be transmitted in m rounds to “inform P _𝒲 about υ over one channel.” He showed that C ₂⩽4C_∞+3 and that in general C₂NOT~C_∞. We give a simple example for C₃NOT~C_∞. However, for the new model “inform P_𝒲 over two channels”, four rounds are optimal for this example-a result we conjecture in general. If both P_𝒱 and P_𝒲 are to be informed over two channels about the other outcome, we determine asymptotically the complexities for all sources. In our last model “inform P_𝒱 and P_𝒲 over one channel” for all sources the total number T₂ of required bits is known asymptotically and T_∞ is bounded from below in terms of average degrees. There are exact results for several classes of regular sources. An attempt is made to discuss the methods of the subject systematically