Repeat-accumulate code: Difference between revisions

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{{Short description|Class of error correction codes}}

{{nomore footnotes|date=February 2014}}

In [[computer science]], '''repeat-accumulate codes''' ('''RA codes''') are a low complexity class of [[error-correcting code]]s. They were devised so that their [[ensemble weight distributions]] are easy to derive. RA codes were introduced by Divsalar ''et al.''

In an RA code, an [[information block]] of length <math>{N}</math> is repeated <math>{q}</math> times, scrambled by an [[interleaver]] of size <math>{qN}</math>, and then encoded by a rate 1 [[accumulator (computing)|accumulator]]. The accumulator can be viewed as a truncated rate 1 [[recursive]] convolutional encoder with transfer function <math>{1/(1 + D)}</math>, but Divsalar ''et al.'' prefer to think of it as a block code whose input block <math>{(z_1, \ldots , z_n)}</math> and output block <math>{(x_1, \ldots , x_n)}</math> are related by the formula <math>{x_1 = z_1}</math> and <math>x_i = x_{i-1}+z_i</math> for <math>i > 1</math>. The encoding time for RA codes is linear and their rate is <math>1/q</math>. They are nonsystematic.

==Irregular Repeatrepeat Accumulateaccumulate Codescodes==

Irregular Repeatrepeat Accumulateaccumulate (IRA) Codescodes arebuild aon derivative formtop of repeatthe accumulateideas of (RA) codes. whereIRA replaces the repetitionouter performedcode in theRA inputcode bitswith isa notlow thedensity samegenerator formatrix all bitscode.<ref>{{cite web |first1=Hui |last1=Jin, |first2=Aamod |last2=Khandekar & |first3=Robert |last3=McEliece, "|title=Irregular Repeat-Accumulate Codes."[ |date=2000 |publisher=Department of Electrical Engineering, California Institute of Technology |url=http://www.mceliece.caltech.edu/publications/Brest00.pdf]}}</ref> IRA codes first repeats information bits different times, and then accumulates subsets of these repeated bits to generate parity bits. The irregular degree profile on the information nodes, together with the degree profile on the check nodes, can be designed using density evolution.

Systematic IRA codecodes are considered a form of [[LDPC]] codescode. TheLitigation claimover thatwhether the DVB-S2 standard implements an LDPC code that is a form of an IRA code is currently under litigationongoing.<ref>Hughes Satellite Codes Spark Caltech Patent Suit.[http://www.law360.com/articles/622198/hughes-satellite-codes-spark-caltech-patent-suit Hughes Satellite Codes Spark Caltech Patent Suit]</ref> US patents 7,116,710; 7,421,032; 7,916,781; and 8,284,833 are at issue.{{cn|date=August 2021}}

==Notes==

{{reflist}}

== References ==

* {{cite conference |first1=D. |last1=Divsalar, |first2=H. |last2=Jin, and |first3=R. J. |last3=McEliece. "|title=Coding theorems for ‘turbo'turbo-like’like' codes." ''Proc.|book-title=Proceedings of the 36thannual Allerton Conf.Conference on Communication, Controlcontrol and Computing, Allerton,|date=September Illinois'',1998 Sept.|pages=201–210 1998,|volume=36 pp|publisher=University Of Illinois |url=https://www.&nbsp;201–210researchgate.net/publication/243768674}}

== External links ==

* [http://www.cambridge.org/gb/knowledge/isbn/item2711886/?site_locale=en_GB Iterative Error Correction: Turbo, Low-Density Parity-Check, and Repeat-Accumulate Codes]

[[Category:Error detection and correction]]

[[Category:Computer languages]]