On Optimal Analog Repeater Systems

In this paper, the optimal analog repeater system which transmits maximum mutual information (MI-system) is discussed. The solution is obtained by conventional variational method and the functional structure of the resulting optimal system is investigated. The system consists of a whitening filter, an "equivalent cable," and a "system equalizer," the concepts of which are newly introduced and defined in the paper. For comparison, the repeater system with minimum mean-square error (ME-system) is analyzed by the analogous method. It is shown that the whitening filter and the "equivalent cable" are invariant for both systems and that the only part which varies with the optimizing criterion is the "system equalizer." Finally, these results are applied to the special case of single stage and the relation to Shannon's water pouring theorem is discussed.