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Timing in a Long Chain of Regenerative Binary Repeaters

01 November 1958

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Regenerative binary repeaters have recently been proposed for both baseband and carrier pulse code modulation s y s t e m s , 1 ' 3 ' 4 in which the signal is represented by a binary pulse train. This type of repeater a t t e m p t s to remove noise and other types of distortion from the incoming pulse train and to transmit a new signal which resembles the original as closely as possible. Noise and other system imperfections have two unwanted effects: (1) a certain number of errors occur at each repeater, i.e., a received pulse is transmitted as a space, or vice versa-, (2) the signal pulses are no longer centered in equally spaced time slots b u t have a random position modulation, called timing noise. T h e present paper is concerned with some of the statistical properties of the random timing deviations in a system containing a long chain of regenerative repeaters. 1543 1.544 T H E BELL SYSTEM T E C H N I C A L J O U R N A L , NOVEMBER 1958 A portion of a typical pulse train under ideal conditions is shown in Fig. 1, where, for purposes of illustration, the individual signal pulses have been made short enough so t h a t they do not overlap; the curve represents either the amplitude of a baseband pulse train or the envelope of a carrier pulse train. T h e pulses are either "011" or "off", denoted by " 1 " and " 0 " respectively; all signal pulses present have a standard amplitude and identical shape, and are centered in equally spaced time slots. A11 ideal regenerative repeater would sample the pulse train of Fig.