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Upon receiving a possibly corrupted w, the receiver checks the parity for the rows and
columns by computing the sum of the appropriate data bits and the corresponding parity
bit (all arithmetic in F2 ). This sum will be 1 if there is a parity error. Then:
• If there are no parity errors, then there has not been a single error, so the receiver can
use the data bits as-is for M . This situation is shown in Figure 6-4(a).
• If there is single row or column parity error, then the corresponding parity bit is in
error. But the data bits are okay and can be used as-is for M . This situation is shown
in Figure 6-4(c), which has a parity error only in the fourth column.
• If there is one row and one column parity error, then the data bit in that row and
column has an error. The decoder repairs the error by ﬂipping that data bit and then
uses the repaired data bits for M . This situation is shown in Figure 6-4(b), where
there are parity errors in the ﬁrst row and fourth column indicating that d14 should
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
- Fall '13