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Burst error-correcting code. In coding theory, burst error-correcting codes employ methods of correcting burst errors, which are errors that occur in many consecutive bits rather than occurring in bits independently of each other. Many codes have been designed to correct random errors.
A cyclic redundancy check ( CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. [1] [2] Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents.
The cyclic redundancy check (CRC) is based on division in the ring of polynomials over the finite field GF (2) (the integers modulo 2 ), that is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around. Any string of bits can be interpreted as the coefficients of a message polynomial of this ...
Turbo code; Walsh–Hadamard code; Cyclic redundancy checks (CRCs) can correct 1-bit errors for messages at most bits long for optimal generator polynomials of degree , see Mathematics of cyclic redundancy checks § Bitfilters; See also. Burst error-correcting code; Code rate; Erasure codes
Code fragment 8: Byte-at-a-time CRC table generation, LSB first. In these code samples, the table index i + j is equivalent to i xor j; you may use whichever form is more convenient. CRC-32 algorithm. This is a practical algorithm for the CRC-32 variant of CRC.
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The first element of a CIRC decoder is a relatively weak inner (32,28) Reed–Solomon code, shortened from a (255,251) code with 8-bit symbols. This code can correct up to 2 byte errors per 32-byte block. More importantly, it flags as erasures any uncorrectable blocks, i.e., blocks with more than 2 byte errors.
Single-error-correcting codes alone can't correct such bursts, so either the convolutional code and the Viterbi decoder must be designed powerful enough to drive down errors to an acceptable rate, or burst error-correcting codes must be used. Punctured codes. A hardware viterbi decoder of punctured codes is commonly implemented in such a way: