On interactive communication - Ahlswede, R.; Cai, N.; Zhang, Z. (IEEE transactions on information theory, 1997)
Ahlswede has previously introduced an abstract correlated source (/spl Vscr//spl times//spl Wscr/,S) with outputs (/spl upsi/, /spl omega/)/spl isin/S/spl sub//spl Vscr//spl times//spl Wscr/, where persons P/sub /spl Vscr// and P/sub /spl Wscr// observe /spl upsi/ and /spl omega/, respectively. More recently, Orlitsky considered the minimal number C/sub m/ of bits to be transmitted in m rounds to "inform P/sub /spl Wscr// about /spl upsi/ over one channel." He showed that C/sub 2//spl les/4C/sub /spl infin//+3 and that in general C/sub 2/NOT/spl sim/C/sub /spl infin//. We give a simple example for C/sub 3/NOT/spl sim/C/sub /spl infin//. However, for the new model "inform P/sub /spl Wscr// over two channels", four rounds are optimal for this example-a result we conjecture in general. If both P/sub /spl Vscr// and P/sub /spl Wscr// 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/sub /spl Vscr// and P/sub /spl Wscr// over one channel" for all sources the total number T/sub 2/ of required bits is known asymptotically and T/sub /spl infin// 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.