Error-detecting codes: parity and CRC
Detecting a transmission error: the parity bit and what it lets through, then the cyclic redundancy check, from the generator polynomial to the remainder of the modulo-2 division appended to the frame.
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Redundancy: what is it?
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Information added to the data, computable from it, which tells nothing new but lets an alteration be spotted.
On reception, this information is recomputed and compared with the one received: if they differ, the frame was altered. Without it, no error shows.
How is the generator x³ + x + 1 written as a binary word?
1011110101111110
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1011Read the coefficients of x³, x², x and 1: 1, 0, 1, 1.
1101is x³ + x² + 1, and0111leaves out the highest-degree term, which defines the polynomial.An even-parity bit is chosen so that the number of 1s in the word is …; it detects any … number of flipped bits.
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An even-parity bit is chosen so that the number of 1s in the word is even; it detects any odd number of flipped bits.
A flipped bit turns an even count of 1s into an odd one: the receiver sees it. Two flips cancel out and go unnoticed.
Parity bit: what is it?
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A bit added to a word so that its total number of 1s is even (even parity) or odd (odd parity).
For 1011011, which has five 1s, the even-parity bit is 1 (reaching six) and the odd-parity bit is 0 (staying at five).