EFFICIENT CODING 



743 



It is often argued that linear predietion is therefore uothin"; more than 

 pre-distortion (freciueiicj^-wisc). If the message is unquantized and un- 

 sampled, and if the signal from the predictor is applied to the channel 

 as straiglit amplitude or single side-band modulation, the allegation is 

 certainly true. Pre-distortion is a perfectly valid way of improving the 

 statistical match between message, and channel, and destination as the 

 optimum filter theory of Weiner and Lee shows. On the other hand, 

 when the message is sampled and quantized, and when the output of 

 the linear predictor is further encoded into a sequence of binary digits, 

 and these are possibly remapped onto a higher base for the channel, then 

 the information is being handled digitally throughout, and the usual 

 reasons for a certain type of predistortion no longer apply. The best 

 linear predictor will usually be quite different for the two cases. Even 

 though analogue operations (such as subtraction of amplitudes) are used 

 for convenience, the quantization makes the operation discrete and 

 hence equivalent to a digital process. 



At the beginning of this section, we were a little vague as to whether 

 the prediction should shift the modes or the means of the conditional 

 distributions to zero amplitude. If the object of the prediction-subtrac- 

 tion operation is to minimize the power in the error signal, then certainly 

 the means should be shifted to zero. The coefficients as determined from 

 the autocorrelation function do this aside from quantizing granularity. 

 They specify an optimum least-square predictor, i.e., one which tends 

 to minimize e, = ^ifp(j)- 



TERMINATION 



ISOLATING 

 AMPLIFIERS 



COEFFICIENT 

 MAGNITUDES 



DIFFERENTIAL 

 SUMMING AMPLIFIER 



IF PRESENT SAMPLE IS SUBTRACTED, OUTPUT WILL 

 BE "ERROR" SIGNAL 



IF PRESENT SAMPLE IS OMITTED, OUTPUT WILL 

 BE ''PREDICTION " 



Fig. 7 — A linear predictor. 



