Error Probabilities in Data System Pulse Regenerator with DC Restoration

In this paper, we consider a binary pulse regenerator with dc restoration (Fig. 1). This system has the property that in the absence of noise it functions error-free. To evaluate the performance of the system, one would like to know the probability of occurrence for an arbitrary error pattern when noise is introduced. This is highly desirable especially if the information coding places high penalty on certain error patterns. It will be shown in this paper that the limiting probability of any error burst can be computed by an iterative procedure. The mathematical theory justifying the validity of the procedure is somewhat involved and will be given in a separate paper on Random Walk in Compact Metric Space.1 Our considerations apply to the data transmission system represented by the block diagram given in Fig. 1. The input sequence dk of random ± 1 impulses goes through a high-pass filter. The output of this filter is 979 980 T H E B E L L SYSTEM TECHNICAL J O U R N A L , J U L Y - A U G U S T 1966