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In fact, a few protocols use the CRC as the message delimiter, a technique called CRC-based framing. (This requires multiple frames to detect acquisition or loss of framing, so is limited to applications where the frames are a known length, and the frame contents are sufficiently random that valid CRCs in misaligned data are rare.)
To compute an n-bit binary CRC, line the bits representing the input in a row, and position the (n + 1)-bit pattern representing the CRC's divisor (called a "polynomial") underneath the left end of the row. In this example, we shall encode 14 bits of message with a 3-bit CRC, with a polynomial x 3 + x + 1.
The simplest checksum algorithm is the so-called longitudinal parity check, which breaks the data into "words" with a fixed number n of bits, and then computes the bitwise exclusive or (XOR) of all those words. The result is appended to the message as an extra word.
To further confuse the matter, the paper by P. Koopman and T. Chakravarty [1] [2] converts CRC generator polynomials to hexadecimal numbers in yet another way: msbit-first, but including the coefficient and omitting the coefficient. This "Koopman" representation has the advantage that the degree can be determined from the hexadecimal form and ...
Name Length Type BSD checksum (Unix) 16 bits sum with circular rotation SYSV checksum (Unix) 16 bits sum with circular rotation sum8 8 bits sum
The code-rate of a given ECC system is defined as the ratio between the number of information bits and the total number of bits (i.e., information plus redundancy bits) in a given communication package. The code-rate is hence a real number.
A parity bit is a bit that is added to a group of source bits to ensure that the number of set bits (i.e., bits with value 1) in the outcome is even or odd. It is a very simple scheme that can be used to detect single or any other odd number (i.e., three, five, etc.) of errors in the output.
CRC Handbook of Chemistry and Physics, a science reference handbook published by CRC Press CRC Standard Mathematical Tables , a mathematics reference handbook published by CRC Press Cyclic redundancy check , a type of hash function used to produce a checksum in order to detect errors in data storage or transmission