Binary codes based on Reed Solomon code. • Field extension. 2 Concatenated Codes [Forney ’66]. Concatenated codes are generated from. If you are interested in collecting all of the obscure books on information theory, this is a must purchase. Forney, the inventor of “concatenated codes,” first. Concatenated Codes [Jr G. Davis Forney] on *FREE* shipping on qualifying offers.
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Views Read Edit View history. Secondly, the NASA standard incorporated an interleaver to spread out bursts of errors, because the errors out of a Viterbi decoder are somewhat bursty, and also because real space channels can suffer other kinds of burst errors. The field of channel coding was revolutionized by the invention of turbo codes by Berrou et al. X band S band K u band K band K a band. In other words, it is N O 1 i.
Concatenated error correction code
The main idea is that if ocncatenated inner block length is selected to be logarithmic in the size of the outer code then the decoding algorithm for the inner code may run in exponential time of the inner block length, and we can thus use an exponential-time but optimal maximum likelihood decoder Forneg for the inner code.
It is understood that polynomial running time here means that running time is polynomial concatdnated the final block length. Turbo codesas described first inimplemented 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.
Iterative decoding was used as follows: When the primary antenna failed to deploy on the Galileo mission to Jupiter inheroic engineering concatebated were undertaken to design the most powerful concatenated code conceived up to that time, and to program it into the spacecraft computers. While concatenated codes showed that the performance-complexity tradeoff problem of channel coding could be solved in principle, they were hardly practical in the technology concatejated the s.
Iterated decoding concatehated now also applied to serial concatenations in order to achieve higher coding gains, such as within serially concatenated convolutional codes SCCCs. The Justesen codes are examples of generalized concatenated codes, where the outer code is a Reed—Solomon code.
In coding theoryconcatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. Turbo codesViterbi algorithm. Any such code may be regarded as a possibly elaborate concatenated code. Transactions on Information Theory. Retrieved from ” http: This page was last edited on 10 Augustat From Wikipedia, the free encyclopedia. Service-oriented architecture Message Abstraction Layer.
McEliece ; Laif Swanson 20 August A natural concept for a decoding algorithm for concatenated codes is to first decode the inner code and then the ofrney code. Although a simple concatenation scheme was implemented already for the Mariner Mars orbiter mission,  concatenated conctaenated were starting to be regularly used for deep space communication with the Voyager programwhich launched two space probes in Originally introduced by Forney in to address a theoretical issue, they became widely used in space communications in the s.
Compared to the elaborate Galileo system described above, this simple RA system is much easier to decode, and, quite amazingly, performs better! The author recalls much eye-rolling when he presented concatenated codes to a Bell Labs research group inand discussed code lengths up into the thousands.
In a looser sense, any serial combination of two or more codes may be referred to as a concatenated code. Then the decoding algorithm is a two-step process:. Turbo codes and other modern capacity- approaching codes may be regarded as elaborations of this approach.
This property can be easily shown based on the idea of defining a generator matrix for the concatenated code in terms of the generator matrices of C out and C in. A simple concatenation scheme is also used on the compact disc CDwhere an interleaving layer between two Reed—Solomon codes of different sizes spreads errors across various blocks.
In his doctoral thesisDave Forney showed that concatenated codes could be used to achieve exponentially decreasing error probabilities at all data rates less than capacity, with decoding complexity that increases only polynomially with the confatenated block length.
Now fornet have to find a polynomial-time decoding algorithm for the inner code.
concatenates The outer code was chosen to be a powerful error-correcting Reed-Solomon code of length over the finite field with elements. However, a key aspect of turbo codes is their iterated decoding approach. Dave ForneyScholarpedia, 4 2: Error detection and correction Coding theory Finite fields Information theory. Retrieved from ” https: Consultative Committee for Space Data Systems. Views Read View concatenatted View history. An early form of iterated decoding was implemented with two to five iterations in the “Galileo code” of the Galileo space probe.
Concatenated codes – Scholarpedia
Typically, the inner code is not a block fornye but a soft-decision convolutional Viterbi-decoded code with a short constraint length. The combination of an inner Viterbi convolutional code with an outer Reed—Solomon code known as an RSV code was first used in Voyager 2  and it became a popular construction both within and outside of the space sector.
In a generalization of above concatenation, there are N possible inner codes C ini and the i -th symbol in a codeword of C out is transmitted across the inner channel using the i -th inner code.