Some Considerations of Error Bounds in Digital Systems

In digital transmission systems the transfer characteristics of the transmitting and receiving filters are far from ideal, and the real transmission channel usually exhibits some form of time dispersion.1'2 When an ideal digital signal is passed through such filters or is transmitted through such a channel, the successive pulses overlap; this form of distortion is usually known as intersymbol interference. Intersymbol interference may also result from the choice of nonoptimum sampling instants, imperfect demodulating-carrier phase, improper pulse design, etc. In addition the signal may be corrupted by thermal noise, cochannel and adjacent channel interference, and other forms of noise that may be present in the channel or in the system used to transmit the information. In digital transmission systems, one of the main performance char3127 3142 THE BELL .SYSTEM TECHNICAL JOURNAL, DECEMBER 1971 acteristics is the probability of error; this probability of error can often be expressed as a finite weighted sum of one or more distribution functions. Various authors have tried to evaluate this probability of error by a variety of methods,2-14 but this highly complex probability distribution can seldom be exactly computed. Simulation techniques that may be used to solve this and other similar problems are never exact since one is constrained to use only a finite number of pulses and no bounds to the truncation error have been derived.* Another method is an analysis by means of a worst-case or "eye pattern" analysis.