Lecture 8 of the Theoretician ' s Toolkit Error - Correcting Codes
نویسنده
چکیده
If a message is sent in plain text, any single error may prevent us from recovering the original message. Such as sending cat and receiving rat . To circumvent this, redundant bits of information can be introduced to identify and correct errors. A simple example of encoding for this purpose would be to send each symbol thrice. To decode a received message (possibly with errors), one could look at every group of three symbols and taking it to mean whichever symbol appears the most often. For example, if we wish to send cat , we actually send cccaaattt . If the received message reads rccaaattt , the decoding scheme successfully recovers cat since the c's still outnumber the r 's. This scheme is able to correct a single error at the expense of blowing up the message size by a factor 3, or, in other words, its information rate is 1/3. This coding scheme is e cient ; we can easily implement this encoding and decoding scheme in, e.g., time polynomial in the original message length. In this lecture, we will see how to e ciently correct an arbitrary, but xed, number of errors with considerably better rate.
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