750 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1952 



incorrectly. If 7i-gramming or prediction is used, then an error in trans- 

 mission will cause the receiver to function improperly not only for that 

 symbol, but its further n-gram decoding or prediction will also be dis- 

 turbed. Thus errors of transmission are either spread over definite blocks, 

 or propagate for a considerable time rather than being confined to the 

 particular symbols sent in error. In fact, if the encoding were completely 

 efficient, all received sequences would be possible messages, and a single 

 error could convert the received message from the proper one into a 

 completely different but possible one. With no redundancy there is 

 no way to recognize an error. It is for these reasons that we have assumed 

 a rugged (quantized) channel. In view of the eight to ten db more average 

 power required in a quantized channel to achieve the same channel 

 capacity as an ideal channel of the same bandwidth, considerable statis- 

 tical saving must be possible before statistical coding may be warranted. 

 This initial handicap of course does not apply to channels already de- 

 signed to work on a digital basis for other reasons. Lastly, the use of 

 error correcting codes^ is a possibility. In these codes a small amount of 

 redundancy is introduced in a particularly efficient fashion. As a result, 

 a certain frequency of transmission errors can be tolerated without 

 causing errors in the reproduced message. 



REFERENCES 



1. Oliver, Pierce, and Shannon, "The Philosophy of PCM," Proc. Inst. Radio 



Engrs., Nov. 1948. 



2. C. E. Shannon, "A Mathematical Theory of Communication," Bell System 



Tech. J., July and Oct. 1948; Shannon and Weaver, "The Mathematical 

 Theory of Communication," University of Illinois Press, 1949. 



3. C. E. Shannon, "Prediction and the Entropy of Printed English," Bell System 



Tech. J., Jan. 1951. 



4. R. W. Sears, "Electron Beam Deflection Tube for Pulse Code Modulation," 



Bell System Tech. J., Jan. 1948; W. M. Goodall, "Television by Pulse Code 

 Modulation," Bell Systeyn Tech. J., Jan. 1951. 



5. R. W. Hamming, "Error Detecting and Error Correcting Codes," Bell System 



Tech. J., Apr. 1950. 



