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{{more 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
Irregular
Systematic IRA codes are considered a form of [[LDPC]] code. Litigation over whether the DVB-S2 LDPC code is a form of IRA code is ongoing.<ref>[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}}
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== References ==
* {{cite conference |first1=D. |last1=Divsalar
== External links ==
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