1008 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



tion, in the absence of noise. In idealized communication theory, charac- 

 teristic distortion has been disregarded in determining channel capacity 

 on the premise that unlike random noise it is predictable and can there- 

 fore be corrected, at least in principle. In actual systems, however, com- 

 plete elimination though possible in principle caimot be accomplished in 

 practice. The resultant limitation on transmission capacity may be as 

 important as that imposed by the maximum signal power that can 

 actually be provided to override noise. 



In the following it will be assumed that correction of amplitude and 

 phase deviations is made by equalization, so that the amplitude and 

 phase characteristics are as assumed for an ideal channel, except for 

 small fine structure residual deviations as illustrated in Fig. 30. These 

 small fine structure deviations may be regarded as of random nature in 

 the sense that they differ among channels and cannot be predicted, 

 although for a given system they would remain fixed in the absence of 

 temperature variations or changes in amplifiers -with age. 



From equation (13.12) it follows that the maximum number of pulse 

 amplitudes or quantizing levels as limited by characteristic distortion is 

 obtained from the relation 



1 



= kUA/An.^ , (16.03) 



or 



9=1 + ^ Axnax/4- (16.04) 



In the absence of characteristic distortion, the maximum number of 

 pulse amplitudes as limited by an rms noise amplitude An or a peak 

 noise amplitude kAn is obtained from the following relation for a bal- 

 anced pulse system. 



^"''" kAn , (16.05) 



q- 1 



or 



g = 1 + -^ ^max/4. (16.06) 



KiAn 



Comparison of (16.04) and (16.06) shows the following equivalence 

 between intersymbol interference and noise from the standpoint of 

 limitation on the permissible number of pulse amplitudes 



U = A„/A, (16.07) 



