Transmission time and bandwidth in pulse code modulation (application of the statistical thermodynamic formalism)

Employing the statistical thermodynamic formalism developed in an earlier paper, it is possible to determine compact sets of transmission times for the words of PCM (pulse code modulation) messages. In particular, we deal with pulses of zero or unit heights. These compact signals, which lead to shorter message times and eliminate redundancy even when successive words are correlated (Markov source), may, however, require additional bandwidth. We examine two simple cases where autocorrelation functions, and therefore power spectra, can be evaluated. In one case, that of the Markov source, it proves possible to accomplishboth shorter transmission time and narrower bandwidth (half-width of the power spectrum), showing that optimization of transmission times can be very worthwhile. Techniques for deriving autocorrelation functions are discussed at length.