G5() THE BELL SYSTEM TECHNICAL JOiniXAL, MAY 1957 



Use of a binary number representation permits the encoded trans- 

 mission of the A^ possible quantized amphtudes in terms of groups of 

 on-off pulses containing n binary digits per code group (where A^ = 

 2").* These pulses may be considered impervious to noise in the trans- 

 mission medium in the sense that complete information is conveyed by 

 the mere recognition of the presence or absence of a pulse rather than a 

 determination of a precise magnitude. Consequently such pulses may, 

 in principle, repeatedly be regenerated in the transmission medium, 

 pro\-ided that regeneration occurs before the on-off pulses have been 

 rendered indistinguishable from each other by noise. 



The designation pulse code modulation (PCM) may therefore be used 

 synonymously with quantized pulse modulation to distinguish the lat- 

 ter from the previously defined varieties of unquantized pulse modula- 

 tion. In view of the restriction of present interest to the role of quantiza- 

 tion per se, there is no need to proceed beyond the choice of quantized 

 PAM as the prototype PCM signal in this discussion, in spite of the fact 

 that PDM and PPM may also be quantized to yield PCM.i 



B. Quantizing Impairment in PCM Systems 



From the foregoing it is clear that quantization (i.e., the representa- 

 tion of a bounded continuum of values by a finite number of discrete 

 magnitudes), permits the encoded, and therefore essentially noise-free 

 transmission of approximate, rather than exact values of sampled ampli- 

 tudes. In fact, the deliberate error imparted to the signal by quantization is 

 the significant source of PCM signal impairment}'^ Adequate limitation 

 of this quantization error is therefore of prime importance in the appli- 

 cation of PCM to communication systems. 



A number of methods of reducing quantizing error suggest themselves 

 on a purely qualitative and intuitive basis. For example, one may obtain 

 a finer-grained approximation by providing more, and therefore smaller, 

 quantizing steps for a given range of amplitudes. Alternative!}', one 

 may provide a more complete description of the signal by increasing the 

 sampling rate beyond the minimum information-theoretic value already 



assumed, t 



It is also possible to vary the size of the quantizing steps (without 

 adding to their number) so as to provide smaller steps for weaker signals. 



* Of course, number representations using a base, h, other than two, so that 

 N = 6", are also avaihible. These are presently of academic interest in view of the 

 increased complexity of instrumentation they imply. ^ 



t See Fig. 5 of Reference 2 for a quantitative evaluation of the efficacy of this 

 measure. 



