Non-Binary Error Correction Codes

l.i Use of Error Correction Codes One function of an error correction code is to aid in the correct transmission of digital information over a noisy channel. This process is illustrated in Fig. 1. An information source gives information to an encoder; the encoder converts the information into a message containing sufficient redundancy to permit the message to be slightly mutilated by the noisy channel and still be correctly interpreted at the destination. The message is then sent via the noisy channel to a decoder which will * This paper was submitted to Columbia University in partial fulfillment of the requirements for the degree of Doctor of Engineering Science in the F a c u l t y of Engineering. 1341 1.348 THE HELL SYSTEM T E C H N I C A L J O U R N A L , N O V E M B E R 1957 reconstruct the original information if the mutilation has not been excessive. 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 b different symbols instead of the usual 1 and 0 of a binary channel.