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 non-errors) 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