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Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, contains chapters on elementary error-correcting codes; on the theoretical limits of error-correction; and on the latest state-of-the-art error-correcting codes, including low-density parity-check codes, turbo codes, and fountain codes.
The advantage of choosing a primitive polynomial as the generator for a CRC code is that the resulting code has maximal total block length in the sense that all 1-bit errors within that block length have different remainders (also called syndromes) and therefore, since the remainder is a linear function of the block, the code can detect all 2 ...
In computer science the parity stripe or parity disk in a RAID provides error-correction. Parity bits are written at the rate of one parity bit per n bits, where n is the number of disks in the array.
An alarm is a persistent indication of a fault that clears only when the triggering condition has been resolved. A current list of problems occurring on the network component is often kept in the form of an active alarm list such as is defined in RFC 3877, the Alarm MIB. A list of cleared faults is also maintained by most network management ...
This is the case in computer memory (usually RAM), where bit errors are extremely rare and Hamming codes are widely used, and a RAM with this correction system is an ECC RAM . In this context, an extended Hamming code having one extra parity bit is often used.
Proof. Let be a codeword with a burst of length .Thus it has the pattern (,,,,,), where and are words of length Hence, the words = (,,,,,) and = (,,,,,) are two ...
Cyclic codes can be linked to ideals in certain rings. Let = [] / be a polynomial ring over the finite field = ().Identify the elements of the cyclic code with polynomials in such that (, …,) maps to the polynomial + + +: thus multiplication by corresponds to a cyclic shift.