Multiterminal estimation theory with binary symmetric source

The multiterminal estimation theory discuss the maximum Fisher information under the Shannon information restriction. In the single-terminal case, it is trivial problem because the maximum Fisher information can be attained at asymptotically 0-rate. Han and Amari (1993) discuss this problem generally and give the lower bound of the maximum Fisher information under rate restriction. Its approach is based on Slepian-Wolf type rate region. We give an example, binary symmetric case, which shows that sufficient statistics can be sent at the rate outside of SW-region using Korner and Morton´s (1979) method, giving a better bound than the one of Han and Amari. Finally we give the general form of such parametric family of which sufficient statistics can be sent at the rate used in the KM type region