Unformatted text preview: detect single errors because the set of code words w (each
deﬁned as M · parity(M )) has a Hamming distance of 2.
If we transmit w when we want to send some message M , then the receiver can take the
received word, r, and compute parity(r) to determine if a single error has occurred. The
receiver’s parity calculation returns 1 if an odd number of the bits in the received message
have been corrupted. When the receiver’s parity calculation returns a 1, we say there has
been a parity error.
This section describes a simple approach to building a SEC code by constructing multiple parity bits, each over various subsets of the message bits, and then using the resulting
parity errors (or nonerrors) to help pinpoint which bit was corrupted.
Rectangular code construction: Suppose we want to send a k bit message M . Shape the
k bits into a rectangular array with r rows and c columns, i.e., k = rc. For example, if
k = 8, the array could be 2 × 4 or 4 × 2 (or even 8 × 1 or 1 × 8, though those are a little
less interesting). Lab...
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 Fall '13
 HariBalakrishnan

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