Synchronizability of a General Class of PCM Formats, Including NRZ, Manchester, and Miller Coding

This paper deals with a general class of PCM formats, which includes the well-known NRZ, Manchester, and Miller coding. We show that the Cramér-Rao lower bound on the mean-square error, resulting from a synchronizer which estimates the delay of a noisy PCM waveform, is inversely proportional to a quantity which depends on the PCM format only. This quantity is termed the "synchronizability" of the PCM format. For the general class of PCM formats we consider in this paper, we obtain as a simple result that the synchronizability equals four times the mean number of zero-crossings of the PCM waveform during one symbol period. Numerical results are presented for NRZ, Manchester, and Miller coding.