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Error Correction (6.4)

Error Correction (6.4). CSE 3213 Fall 2011. Error Correction. Given a data block/frame of k bits, we map each k-bit sequence into a unique n-bit codeword, and k < n. Hamming distance d(v 1 , v 2 ): the number of bits in which v 1 and v 2 disagree.

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Error Correction (6.4)

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  1. Error Correction (6.4) CSE 3213 Fall 2011

  2. Error Correction • Given a data block/frame of k bits, we map each k-bit sequence into a unique n-bit codeword, and k < n. • Hamming distance d(v1, v2): the number of bits in which v1 and v2 disagree. • Example: v1= 011011, v2 = 110001, d(v1, v2) = 3

  3. Example Assume the received coded block is 00100.

  4. Invalid Codewords

  5. Hamming Distances • Between valid codewords • Min distance between valid codewords is 3. • The code can always correct a single-bit error. • Can always detect a double-bit error (but cannot correct it).

  6. In general … • dmin = minimum distance between valid codewords. • The code can correct all bit errors up to and including errors of t bits where t = I_ (dmin ─1) / 2 _I • The code can detect all bit errors up to and including errors of t bits where t = dmin ─1

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