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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.
When this occurs, it is often possible to fix the issue by switching the character encoding without loss of data. The situation is complicated because of the existence of several Chinese character encoding systems in use, the most common ones being: Unicode , Big5 , and Guobiao (with several backward compatible versions), and the possibility of ...
Reed & Solomon (1960) described a theoretical decoder that corrected errors by finding the most popular message polynomial. The decoder only knows the set of values to and which encoding method was used to generate the codeword's sequence of values. The original message, the polynomial, and any errors are unknown.
Since the source is only 4 bits then there are only 16 possible transmitted words. Included is the eight-bit value if an extra parity bit is used (see Hamming(7,4) code with an additional parity bit).
The fact that errors appear as "bursts" should be accounted for when designing a concatenated code with an inner convolutional code. The popular solution for this problem is to interleave data before convolutional encoding, so that the outer block (usually Reed–Solomon) code can correct most of the errors.
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Hadamard code is a [,,] linear code and is capable of correcting many errors. Hadamard code could be constructed column by column : the i t h {\displaystyle i^{th}} column is the bits of the binary representation of integer i {\displaystyle i} , as shown in the following example.