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The purpose of this paper is to derive the optimum word length for the simultaneous digital transmission of a number of continuous signals in real time, through a single communication channel. The transmission introduces sampling and quantization errors; the relation between the fineness of the quantization and the sampling rate, as a function of word length, for a given capacity of the channel, is investigated. Individual word length for signals having different amplitude distribution and unequal expected frequency is also derived. It is assumed that the functions to be transmitted have known statistical properties. An example is worked out in detail for the case of normal distribution of amplitudes of the transmitted signals. The investigation is carried out for the case when a zero-order hold circuit is used for the reconstruction of the signals, and the results are compared with the case of an optimum linear reconstruction circuit.