PCM Transmission with Minimum Mean-Square Error

One source of error in PCM transmission of analog waveform is the bit errors made in the binary sequences representing a particular level. Using a mean-square error criterion, the contribution of this (channel) error to the overall reconstruction error is examined. In particular, general simplified error expressions are derived for arbitrary sequence assignments including error correcting coding. Results are given for the power gain resulting from use of several error correcting codes. The criterion used here is meansquare error (rather than word probability of error) and the coded sequence is constrained to occupy the same time interval as the uncoiled sequence.