1374 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



In this example, an information source generates n quinary and n — m 

 binary information digits for each message. All quinary digits go through 

 an odd or even recognition circuit to be converted into binary digits for 

 the purpose of generating a binary error correction code message. These 

 binary digits and the binary digits generated by the information source 

 are fed into a systematic binary error correction code encoder whose 

 output is a binary message containing 2n. digits, of which m are parit}^ 

 check digits. This output is divided into two parts, 2n — m original 

 inputs to the encoder unchanged by the encoding process (this is a sys- 

 tematic encoder which does not change information digits in encoding), 

 and m parity check digits. 



The m parity check digits are then combined with m of the quinary 

 information digits through the use of the reflected quibinary combiner 

 to form m of the decimal digits of the decimal message that is trans- 

 mitted; the other decimal digits are formed by combining the n — m 

 binary information digits with the rest of the quinary information 

 digits. 



The decimal message is transmitted over the noisy channel and arrives 

 with one or more (a number limited by the choice of the binary code) 

 errors of ±1 on decimal digits. It is fed into a reflected quibinary resolver 

 which resolves decimal digits into binary and quinary components in 

 accordance with the reflected quibinary code (Table X). The quinary 

 digits are then fed into an odd or even recognition circuit to form binary 

 digits; these and the binary outputs of the resolver are fed into a binary 

 decoder and corrector, working with the same code as the binary en- 

 coder. The output of this corrector should correspond to the output of 

 the original binary encoder. 



In the decoder, the binary digits are corrected. When the binary digit 

 derived from a quinary digit is corrected, however, the quinary digit is 

 not yet correct. The correction of the quinarj^ digit is performed by 

 examining both the corrected binary digit derived from the quinary 

 digit and the corrected binary digit which was deri^'ed from the same 

 decimal digit as the quinary digit in ([uestion. The rules for correcting 

 the quinary digit are given in Table XI. 



As an example, consider the application of a Hamming Code for 

 transmitting ten binary digits in a fourteen binary digit message. 



Using a code of this type, single errors of ±1 may be corrected in a 

 seven digit decimal message, transmitting seven ciuinary digits of in- 

 formation and three binary digits of information. The characteristics 

 required for a fourteen binary digit Hamming Code message are shown 

 in the first column of Table XII. 



