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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]]. 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. | |||
== References == | |||
* D. Divsalar, H. Jin, and R. J. McEliece. "Coding theorems for ‘turbo-like’ codes." ''Proc. 36th Allerton Conf. on Communication, Control and Computing, Allerton, Illinois'', Sept. 1998, pp. 201–210. | |||
== 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]] | |||
Revision as of 06:49, 25 July 2013
In computer science, repeat-accumulate codes (RA codes) are a low complexity class of error-correcting codes. 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 is repeated times, scrambled by an interleaver of size , and then encoded by a rate 1 accumulator. The accumulator can be viewed as a truncated rate 1 recursive convolutional encoder with transfer function , but Divsalar et al. prefer to think of it as a block code whose input block and output block are related by the formula and for . The encoding time for RA codes is linear and their rate is . They are nonsystematic.
References
- D. Divsalar, H. Jin, and R. J. McEliece. "Coding theorems for ‘turbo-like’ codes." Proc. 36th Allerton Conf. on Communication, Control and Computing, Allerton, Illinois, Sept. 1998, pp. 201–210.