Repeat-accumulate code: Difference between revisions

Revision as of 20:19, 17 January 2007

Revision as of 20:23, 17 January 2007

Line 1:

{{Notability|date=December 2006}}

{{Orphan|November 2006}}

In [[computer science]], '''Repeatrepeat-Accumulateaccumulate 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.''

et al. who initially devised the codes because their ensemble weight distributions are

easy to derive.

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.

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,''mis

Sept. 1998, pp. 201–210.