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Unformatted text preview: e appropriate corrective action for each combination of the syndrome
E3 E2 E1
6.4.4 Corrective Action
p1 has an error, ﬂip to correct
p2 has an error, ﬂip to correct
d1 has an error, ﬂip to correct
p3 has an error, ﬂip to correct
d2 has an error, ﬂip to correct
d3 has an error, ﬂip to correct
d4 has an error, ﬂip to correct Is There a Logic to the Hamming Code Construction? So far so good, but the allocation of data bits to parity-bit computations may seem rather
arbitrary and it’s not clear how to build the corrective action table except by inspection.
The cleverness of Hamming codes is revealed if we order the data and parity bits in a
certain way and assign each bit an index, starting with 1:
(7,4) code 1
d4 This table was constructed by ﬁrst allocating the parity bits to indices that are powers
of two (e.g., 1, 2, 4, . . . ). Then the data bits are allocated to the so-far unassigned indicies,
starting with the smallest index. It’s easy to see how...
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
- Fall '13