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A CRC has properties that make it well suited for detecting burst errors. CRCs are particularly easy to implement in hardware and are therefore commonly used in computer networks and storage devices such as hard disk drives. The parity bit can be seen as a special-case 1-bit CRC.
CRC-3-GSM: mobile networks [25] 0x3 0x6 0x5 ... The Blue Book. Systems Research Group, Computer Laboratory, University of Cambridge. Algorithm 4 was used in Linux and ...
One of the most commonly encountered CRC polynomials is known as CRC-32, used by (among others) Ethernet, FDDI, ZIP and other archive formats, and PNG image format. Its polynomial can be written msbit-first as 0x04C11DB7, or lsbit-first as 0xEDB88320.
These inversions are extremely common but not universally performed, even in the case of the CRC-32 or CRC-16-CCITT polynomials. They are almost always included when sending variable-length messages, but often omitted when communicating fixed-length messages, as the problem of added zero bits is less likely to arise.
Interleaving alleviates this problem by shuffling source symbols across several code words, thereby creating a more uniform distribution of errors. [21] Therefore, interleaving is widely used for burst error-correction. The analysis of modern iterated codes, like turbo codes and LDPC codes, typically assumes an independent distribution of ...
Most packet switched networks use store-and-forward transmission at the input of the link. A switch using store-and-forward transmission will receive (save) the entire packet to the buffer and check it for CRC errors or other problems before sending the first bit of the packet into the outbound link. Thus, store-and-forward packet switches ...
[1]: section 3.2.9 An alternative is to calculate a CRC using the right shifting CRC-32 (polynomial = 0xEDB88320, initial CRC = 0xFFFFFFFF, CRC is post complemented, verify value = 0x2144DF1C), which will result in a CRC that is a bit reversal of the FCS, and transmit both data and the CRC least significant bit first, resulting in identical ...
Consequently, the problem is finding the X k, because then the leftmost matrix would be known, and both sides of the equation could be multiplied by its inverse, yielding Y k. In the variant of this algorithm where the locations of the errors are already known (when it is being used as an erasure code), this is the end.