Characteristics of the Hedeman H-1, H-2, and H-3 Codes

This paper examines three new digital modulation binary codes developed by Hedeman and denoted as the H-1, H-2, and H-3 codes. It contains a complete description of the Hedeman codes and analyzes several of their important properties. The bit error probability is displayed as a function of signal-to-noise ratio, and detector implementation is discussed. It is shown that with a maximum likelihood sequence estimator using soft decisions, the H-2 and H-3 codes can achieve the same bit error rate as the nonreturn-to-zero (NRZ) or Manchester codes. Autocorrelation functions and power spectral densities of the Hedeman codes are presented. These results indicate that they possess the favorable quality of no dc component. Finally, symbol synchronization is considered. Here, phase synchronizing template patterns are identified and the probability of resynchronization is given as a function of time after loss of synchronization.