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To understand the advantages, start with the slice-by-2 case. We wish to compute a CRC two bytes (16 bits) at a time, but the standard table-based approach would require an inconveniently large 65536-entry table. As mentioned in § Generating the lookup table, CRC tables have the property that table[i xor j] = table[i] xor table[j].
The CRC and associated polynomial typically have a name of the form CRC-n-XXX as in the table below. The simplest error-detection system, the parity bit , is in fact a 1-bit CRC: it uses the generator polynomial x + 1 (two terms), [ 5 ] and has the name CRC-1.
XOR/table Paul Hsieh's SuperFastHash [1] 32 bits Buzhash: variable XOR/table Fowler–Noll–Vo hash function (FNV Hash) 32, 64, 128, 256, 512, or 1024 bits xor/product or product/XOR Jenkins hash function: 32 or 64 bits XOR/addition Bernstein's hash djb2 [2] 32 or 64 bits shift/add or mult/add or shift/add/xor or mult/xor PJW hash / Elf Hash ...
Turbo coding is an iterated soft-decoding scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
cksum is a command in Unix and Unix-like operating systems that generates a checksum value for a file or stream of data. The cksum command reads each file given in its arguments, or standard input if no arguments are provided, and outputs the file's 32-bit cyclic redundancy check (CRC) checksum and byte count. [1]
All single bit errors within the bitfilter period mentioned above (for even terms in the generator polynomial) can be identified uniquely by their residual. So CRC method can be used to correct single-bit errors as well (within those limits, e.g. 32,767 bits with optimal generator polynomials of degree 16).
Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
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.