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L10 - A fundamental step in error control is to detect the...

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A fundamental step in error control is to detect the presence of errors in a packet or frame. What if errors are detected? One option is to request retransmission. Another option is to find and correct the errors if it can be done with confidence. This is called error correction. Some systems use both: correct errors if feasible, else ask for retransmission.
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Error control can be exercised at the link layer or the end-to-end transport layer, or both. a) A multilink path from A to B with low per link error probability b) A multilink path from A to B with one noisy link. A common case of b) is when there is a noisy wireless link in a path where other wired links have very few errors.
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ERROR DETECTION A frame of data usually includes parity check bits for error detection. k = number of "data" bits in the frame. c = number of checking bits. n = k+c = total frame length, excluding flags. k includes data, overhead, control bits. The only things not checked in the frame are flags, since they are known patterns. 1 2 c Call the check bits P , P , ........ P . The check bits are derived by a linear operation, addition modulo two (exclusive OR). An even number of ones adds to zero. The total n bits with k data bits constitute a (n,k) block code .
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The check symbols are derived by a multiplication of the data vector by a k * c matrix of ones and zeroes. For example, take c = 3 check bits, k = 4 data bits. 1 2 3 1 2 3 4 [ P P P ] = [ D D D D ] 1 1 2 4 Thus P = D + D + D 2 1 3 4 P = D + D + D 3 2 4 P = D + D Practical frames often contain thousands of "data" bits. Matrix multiplication too complex and slow.
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We will see a much quicker and simpler way of computing the check bits.
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  • Spring '11
  • Unknow
  • Hamming Code, Error detection and correction, Parity bit, error detection, Low-density parity-check code, Automatic repeat request

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