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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.
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.
A remedial action is a change made to a nonconforming product or service to address the deficiency. This also can refer to restoration of a landscape from industrial activity [ 1 ] Rework and repair are generally the remedial actions taken on products, while services usually require additional services to be performed to ensure satisfaction.
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 ()).
Let's say three errors corrupt the transmitted bits and the received sequence is 111 010 100. Decoding is usually done by a simple majority decision for each code word. That lead us to 100 as the decoded information bits, because in the first and second code word occurred less than two errors, so the majority of the bits are correct. But in the ...
The distance d was usually understood to limit the error-correction capability to ⌊(d−1) / 2⌋. The Reed–Solomon code achieves this bound with equality, and can thus correct up to ⌊(n−k) / 2⌋ errors. However, this error-correction bound is not exact.
Hadamard code is a [,,] linear code and is capable of correcting many errors. Hadamard code could be constructed column by column : the column is the bits of the binary representation of integer , as shown in the following example.
This book is mainly centered around algebraic and combinatorial techniques for designing and using error-correcting linear block codes. [ 1 ] [ 3 ] [ 9 ] It differs from previous works in this area in its reduction of each result to its mathematical foundations, and its clear exposition of the results follow from these foundations.
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