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Unformatted text preview: ome bits, we can look for the
bits in each code word that appear in all the Ei computations that produced 1; these bits are
potential candidates for having an error since any of them could have caused the observed
parity errors. Now eliminate from the candidates bits that appear in any Ei computations
that produced 0 since those calculations prove those bits didn’t have errors. We’ll be left
with either no bits (no errors occurred) or one bit (the bit with the single error).
For example, if E1 = 1, E2 = 0 and E3 = 1, we notice that bits d2 and d4 both appear
in the computations for E1 and E3 . However, d4 appears in the computation for E2 and
should be eliminated, leaving d2 as the sole candidate as the bit with the error.
Another example: suppose E1 = 1, E2 = 0 and E3 = 0. Any of the bits appearing in the 14 LECTURE 6. COPING WITH BIT ERRORS computation for E1 could have caused the observed parity error. Eliminating those that
appear in the computations for E2 and E3 , we’re left with p1 , which must be the bit with
the error.
Applying this reasoning to each possible combination of parity errors, we can make a
table that shows th...
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 Fall '13
 HariBalakrishnan

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