The class of hamming single error correcting codes is

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Unformatted text preview: ￿ 6.4.3 Hamming Codes Intuitively, it makes sense that for a code to be efficient, each parity bit should protect as many data bits as possible. By symmetry, we’d expect each parity bit to do the same amount of ”work” in the sense that each parity bit would protect the same number of data bits. If some parity bit is shirking its duties, it’s likely we’ll need a larger number of parity bits in order to ensure that each possible single error will produce a unique combination of parity errors (it’s the unique combinations that the receiver uses to deduce which bit, if any, had a single error). The class of Hamming single error correcting codes is noteworthy because they are particularly efficient in the use of parity bits: the number of parity bits used by Hamming 13 SECTION 6.4. LINEAR BLOCK CODES AND PARITY CALCULATIONS d1 p1 p2 d5 d3 p2 d7 d11 d9 d4 d2 d1 p1 d6 d10 d4 d2 d3 d8 p4 p3 p3 (a) (7,4) code (b) (15,11) code Figure 6-6: Venn diagrams of Hamming codes showing which data bits are protected by each parity bit. codes grows logarithmically with the size of the code word. Figure 6-6 shows two examples of the class: the (7,4) and (15,11) Hamm...
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.

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