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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 ...
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.
Automatic repeat request (ARQ), also known as automatic repeat query, is an error-control method for data transmission that uses acknowledgements (messages sent by the receiver indicating that it has correctly received a message) and timeouts (specified periods of time allowed to elapse before an acknowledgment is to be received) to achieve ...
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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.
LDPC encoder. During the encoding of a frame, the input data bits (D) are repeated and distributed to a set of constituent encoders. The constituent encoders are typically accumulators and each accumulator is used to generate a parity symbol.
Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).