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• Other combinations of row and column parity errors indicate that multiple errors
have occurred. There’s no “right” action the receiver can undertake because it
doesn’t have sufﬁcient information to determine which bits are in error. A common
approach is to use the data bits as-is for M . If they happen to be in error, that will be
detected when validating by the error detection method.
This recipe will produce the most likely message, M , from the received code word if there
has been at most a single transmission error.
In the rectangular code the number of parity bits grows at least as fast as k (it should
be easy to verify that the smallest number of parity bits occurs when the number of rows,
r, and the number of columns, c, are equal). Given a ﬁxed amount of communication
bandwidth, we’re interested in devoting as much of it as possible to sending message bits,
not parity bits. Are there other SEC codes that have better code rates than our simple
rectangular code? A natural question to ask is: how...
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- Fall '13