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What framing signal uses a CRC-4?
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In telecommunications, framing signals are used to synchronize data transmission between devices, allowing the receiver to identify the beginning and end of data frames. Show more…
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An efficient error-correcting code. Consider a signal consisting of 16 -bit message blocks accompanied by 8 -bit check blocks; that is, $1 / 3$ of the signal consists of check bits. Each 16 -bit message block is arranged into a $4 \times 4$ array, and the 8 check bits are aligned with the top row and left column of the message, as shown, with the 16 -bit message in the dark square in the lower right. Each check bit is set so that there are an even number of 1 s in every column and every row (in those 4 rows and 4 columns containing message bits). You should verify that this is true for the (message $+$ check) array shown here. (a) Suppose a single-bit error occurs somewhere in the message block. How many check bits will violate the "even sum" rule? How can this information be used to identify and correct the mistake? (b) Suppose a single-bit error occurs somewhere in the check block. How many check bits will violate the "even-sum" rule? How does this information indicate that the error is not in the message, but in the check block? (c) Suppose that $N \times N$ message blocks are used instead of $4 \times 4$ message blocks. How many check bits are required? What fraction of signal bits are check bits? (d) Explain why this simple scheme fails if two errors occur in the same row or column.
Solids-Applications
The Digital Information Age
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