Isye 2027

# Therefore the mean total waiting time until double

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Unformatted text preview: ot 2.12. RELIABILITY 67 detected, which can happen for some nonzero error patterns. It is explained next that any error pattern with either one, two, or three bit errors is detected, but certain error patterns with four bit errors are not detected. An error pattern is undetected if and only if the parity of each row and column is even, which requires that the parity of the entire error pattern be even. Thus, any error pattern with an odd number of bit errors is detected. In particular, error patterns with one or three bit errors are detected. If there are two bit errors, they are either in diﬀerent rows or in diﬀerent columns (or both). If they are in diﬀerent rows then those rows have odd parity, and if they are in diﬀerent columns then those columns have odd parity. So, either way, the error pattern is detected. A pattern with four bit errors is undetected if and only if there are two rows and two columns such that the bit errors are at the four intersections of the two rows and two columns. We now discuss...
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