Detecting and Correcting Errors - MIT

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Fall 2006Detecting and Correcting Errors , Slide 1Detecting andCorrecting Errors Codewords and Hamming Distance Error Detection: parity Single-bit Error Correction Burst Error Correction Fall 2006Detecting and Correcting Errors , Slide 2There s good news and bad good news: Our digital modulation scheme usually allows us to recover the original signal despite small amplitude Errors introduced by the components and example of the digital abstraction doing its job!The bad news: larger amplitude Errors (hopefully infrequent) that change the signal irretrievably.

Parity check fails for row #2 and column #2 ⇒bit D 4 is incorrect 0 1 1 1 1 1 1 0 Parity check only fails for row #2 ⇒bit P 2 is incorrect If we add an overall parity bit P 5,we get a (9,4,4) code! 6.082 Fall 2006 Detecting and Correcting Errors, Slide 14 …

  Parity, Check, Parity check