748 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1952 



be more highly correlated. Thus in TV, doubling the horizontal resolu- 

 tion would not double the bandwidth for the same picture material if 

 use were made of the statistics. (Of course, increased resolution in TV 

 might encourage the use of more detailed scenes and this would increase 

 the required bandwidth.) 



It should also be noticed that for small (, linear prediction actually 

 makes matters worse. The increase in the number of levels in the error 

 signal more than offsets the peaking of the distribution. 



Since all the conditional distributions in this message are of similar 

 shape (after ordering), Hd and H are almost the same, for all /. The 

 difference between H^ and Hd is slight except for small ( because the 

 distribution we assumed is unimodal throughout. 



Fig. 10 shows the simple probability distributions for (a) the original 

 message, (b) the reduced signal from linear prediction, and (c) the re- 

 duced signal from the digrammer. 



VARIABLE DELAY AND OTHER PROBLEMS 



We have seen in the last two sections how it is possible to convert 

 a message for which i7 <<C i/o as a result primarily of intersymbol correla- 

 tion, into a reduced signal for which H « Ho as a result primarily of a 

 highly peaked probability distribution in the individual symbols (i.e. 

 one for which Hi -^ H). Since the operations are reversible, the true 

 information rate, H, is preserved. In the original signal it was the 

 conditional distributions which were peaked, while the simple distribu- 

 tion was relatively flat. In the reduced signal the simple distribution is 

 peaked. 



The result is that whereas a Shannon-Fano code would onty have been 

 effective on the original message if applied to blocks two or more symbols 

 in length (and then it would ignore correlation between blocks), in the 

 reduced signal the code will be effective on a symbol to symbol basis. 



U ^^^LU 



a) u (^) Lu (^) au ^^^ . 1 1 1 1 1 i . 



(b) (b) (b) 



lL , I I I ■ ._l1 



(b) 

 i_^ 



(c) 



J '"Lb 



(c] 



(c) 



J M il.. 



1=2 1=3 1=4 1=8 



Fig. 10 — Probability distributions: (a) Original, (b) After linear modal pre- 

 diction, (c) After digramming. 



