L14_reed_solomon_codes

L14_reed_solomon_codes - Detecting and Correcting Errors...

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6.02 Spring 2008 Detecting and Correcting Errors (Part 2), Slide 1 Detecting and Correcting Errors (Part II) 6.02 Spring 2008 Detecting and Correcting Errors (Part 2), Slide 2 From the Homework… Problem 4 . Ben Bitdiddle woke up in the middle of the night with the following great idea: in order to implement double-bit error correction he would use the (8,4,3) code described in lecture – which can correct single-bit errors –to encode a message twice. In other words, after the message was encoded for the first time with the (8,4,3) code, the resulting bit stream would be re-encoded with the same code a second time. a. If the original message had 80 bits, how many bits will be in the doubly-encoded message? b. Will Ben’s scheme work, i.e., will he be able to correct double-bit errors? Briefly describe why or why not.
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6.02 Spring 2008 Detecting and Correcting Errors (Part 2), Slide 3 In search of a better code Problem: information about a particular message unit (bit, byte, . .) is captured in just a few locations, ie, the message unit and some number of parity units. So a small but unfortunate set of errors might wipe out all the locations where that info resides, causing us to lose the original message unit. Potential Solution: figure out a way to spread the info in each message unit throughout all the codewords in a block. Require only some fraction good codewords to recover the original message. 6.02 Spring 2008
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L14_reed_solomon_codes - Detecting and Correcting Errors...

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