Repeat-accumulate code

Repeat-Accumulate codes (RA codes) are a low complexity class of error-correcting code introduced by Divsalar 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 ${N}$ is repeated ${q}$ times, scrambled by an interleaver of size ${qN}$, and then encoded by a rate 1 accumulator. The accumulator can be viewed as a truncated rate 1 recursive convolutional encoder with transfer function ${1/(1+D)}$, but Divsalar et al. prefer to think of it as a block code whose input block ${(z_{1},\ldots ,z_{n})}$ and output block ${(x_{1},\ldots ,x_{n})}$ are related by the formula ${x_{1}=z_{1}}$ and $x_{i}=x_{i-1}+z_{i}$ for $i>1$. The encoding time for RA codes is linear and their rate is $1/q$. 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.