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All error-detection and correction schemes ... 1010 1010 1010 in the previous example would be detected ... The parity bit is an example of a single-error-detecting ...
The generalized minimum distance algorithm, developed by Forney, can be used to correct up to dD/2 errors. [2] It uses erasure information from the inner code to improve performance of the outer code, and was the first example of an algorithm using soft-decision decoding. [3] [4]
The rate of a block code is defined as the ratio between its message length and its block length: = /. A large rate means that the amount of actual message per transmitted block is high.
They described a systematic way of building codes that could detect and correct multiple random rank errors. By adding redundancy with coding k -symbol word to a n -symbol word, a rank code can correct any errors of rank up to t = ⌊ ( d − 1) / 2 ⌋, where d is a code distance.
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.
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 ()).
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A Reed–Solomon code (like any MDS code) is able to correct twice as many erasures as errors, and any combination of errors and erasures can be corrected as long as the relation 2E + S ≤ n − k is satisfied, where is the number of errors and is the number of erasures in the block.