Quantizing Noise and Data Transmission

Methods for calculating the power in the quantizing noise on digital transmission facilities have been known for some time. A more difficult but unavoidable problem is the effect that this noise has on data signals intended for analog transmission. This paper demonstrates that to assume that the noise will behave as a white Gaussian noise process will always {except for a simple factor) yield an upper bound on the probability of error when no companding is present. We assume that linear detection will be used, as for a PAM system, and the result is true whether or not filtering or demodulation is involved. Results are illustrated by applying them to a model of an existing V SB modem whereby the additional degradations resulting from data set imperfections are included as added baseband noise. A modem operating perfectly woidd make no errors at all at the higher transmission levels. For example, with no companding, a set with an eightlevel eye closed by even 80 percent would not yield errors for input powers down to --15 dBm. Thus quantizing noise is not a basic limiting factor in the error rate for all input levels. A similar rigorous theory is not available for compandored systems, but for special situations reasonable estimates can be made. For logarithmic companding and eight-level VSB transmission, worst case estimates indicate error rates about 10 - 6 for one link of T1 carrier.