1342 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



reconstruct the original information if the mutilation has not been ex- 

 cessive. Finally, the information is sent to an information receptor. 



One scheme for correcting errors in a binary system is to send each 

 binary digit of information three times and to accept at the receiver 

 that value which is represented by two or three of the received digits. 

 Then, the encoder is simply an instrument for causing each digit to be 

 sent three times, and the decoder consists of a majority organ. However, 

 many methods are available which are considerably more elegant, and 

 which will permit more information to be passed through a noisy channel 

 in a given unit of time. This paper will deal with such methods for 

 channels capable of sending h different symbols instead of the usual 1 and 

 of a binary channel. 



The most convenient explanation of an error correction code has been 

 made with respect to the transmission of correct digital information 

 over a noisy channel. This does not imply the restriction of such codes 



NOISE 



Fig. 1 — Transmission over a noisy channel. 



to the noisy channel problem exclusively. Actually, the first application 

 considered for such a code was with respect to computers.^ Many large 

 high speed computers stop whenever an error is detected in some calcu- 

 lation and must be restarted; with the use of an error correction code 

 this could be avoided by permitting the computer to correct its own 

 random errors directly. To the best knowledge of the author, error 

 correction codes have not yet been used in any major computer. But 

 the storage system of a computer may, in the future, lend itself to the 

 use of error correction codes. 



Frequently, very elaborate precautions must be taken in present 

 storage systems to insure that they are free from errors. Magnetic tapes 

 must be specially made and handled to guarantee the absence of defects, 

 magnetic cores must be carefully tested to make sure that no defective 

 cores get into an array, cathode I'ay tubes used in Williams Tube or 

 Barrier Grid Tube storage systems must be perfect. Probably, there are 

 other storage methods whose development is hampered because of a 

 common requirement for error-free performance in all storage locations. 

 With the use of error correction codes, such storage systems could be 

 used, if they are sufficiently close to perfection, even though not perfect. 



