L6_2

# The cleverness of hamming codes is revealed if we

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Unformatted text preview: e appropriate corrective action for each combination of the syndrome bits: E3 E2 E1 000 001 010 011 100 101 110 111 ￿ 6.4.4 Corrective Action no errors 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: index binary index (7,4) code 1 001 p1 2 010 p2 3 011 d1 4 100 p3 5 101 d2 6 110 d3 7 111 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.

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