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A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages.
The description above is given for what is now called a serially concatenated code. Turbo codes, as described first in 1993, implemented a parallel concatenation of two convolutional codes, with an interleaver between the two codes and an iterative decoder that passes information forth and back between the codes. [6]
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If the channel quality is bad, and not all transmission errors can be corrected, the receiver will detect this situation using the error-detection code, then the received coded data block is rejected and a re-transmission is requested by the receiver, similar to ARQ.
An error-correcting code is a way of encoding x as a message such that Bob will successfully understand the value x as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is two-way: Bob can send feedback to Alice about the message he received.
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.
The key innovation of turbo codes is how they use the likelihood data to reconcile differences between the two decoders. Each of the two convolutional decoders generates a hypothesis (with derived likelihoods) for the pattern of m bits in the payload sub-block. The hypothesis bit-patterns are compared, and if they differ, the decoders exchange ...
Verhoeff's notes that the particular permutation, given above, is special as it has the property of detecting 95.3% of the phonetic errors. [8] The strengths of the algorithm are that it detects all transliteration and transposition errors, and additionally most twin, twin jump, jump transposition and phonetic errors.