4.3: Detection vs. Correction

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Page ID: 50172

Paul Penfield, Jr.
Massachusetts Institute of Technology via MIT OpenCourseWare

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There are two approaches to dealing with errors. One is to detect the error and then let the person or system that uses the output know that an error has occurred. The other is to have the channel decoder attempt to repair the message by correcting the error. In both cases, extra bits are added to the messages to make them longer. The result is that the message contains redundancy—if it did not, every possible bit pattern would be a legal message and an error would simply change one valid message to another. By changing things so that many (indeed, most) bit patterns do not correspond to legal messages, the effect of an error is usually to change the message to one of the illegal patterns; the channel decoder can detect that there was an error and take suitable action. In fact, if every illegal pattern is, in a sense to be described below, closer to one legal message than any other, the decoder could substitute the closest legal message, thereby repairing the damage.

In everyday life error detection and correction occur routinely. Written and spoken communication is done with natural languages such as English, and there is sufficient redundancy (estimated at 50%) so that even if several letters, sounds, or even words are omitted, humans can still understand the message.

Note that channel encoders, because they add bits to the pattern, generally preserve all the original information, and therefore are reversible. The channel, by allowing errors to occur, actually introduces information (the details of exactly which bits got changed). The decoder is irreversible in that it discards some information, but if well designed it throws out the “bad” information caused by the errors, and keeps the original information. In later chapters we will analyze the information flow in such systems quantitatively.