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.

It is shown by Shannon that the zero-error capacity of a noisy channel may be increased with feedback. However, feedback cannot improve the zero-error capacity of all memoryless channels. The graphs of discrete memoryless channels are classified on the basis of whether feedback increases the zero-error capacity or not.

This paper reviews recent progress in communication theory in Japan, mainly in the past three years. The topics to be discussed include 1) waveform transmission in band-limited channels and active transmission lines, 2) source-coding problems such as optimal quantizing characteristics, delta modulation, and linear transformation, 3) transmission codes, where mainly multilevel codes have been discussed, 4) new information transmission and modulation schemes, and 5) theories of traffic and switchingsystem design.

A class of binary sequences whose elements are either1or-1and whose autocorrelation function is0for all even shifts except the zero shift is discussed. These sequences will be calledEsequences. It is proved that everyEsequence is paired with anotherEsequence, its mate, so that the cross-correlation function between them is0for all even shifts including the zero shift. Using these sequences, new complete orthogonal function sets are derived. Several other important properties of these sequences are also obtained and the relations among these sequences, Golay's complementary sequences and Welti's quaternary codes are discussed.