# Repeat-accumulate code

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 ${N}$ 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.

## Irregular Repeat Accumulate Codes

Irregular Repeat Accumulate (IRA) Codes are a derivative form of repeat accumulate (RA) codes where the repetition performed on the input bits is not equal for all bits.[1] For example, some bits may be repeated three (3) times during coding, while other bits may be repeated eight (8) times.

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.[2] US patents 7,116,710; 7,421,032; 7,916,781; and 8,284,833 are at issue.

## Notes

1. ^ Hui Jin, Aamod Khandekar & Robert McEliece, "Irregular Repeat-Accumulate Codes."[1]
2. ^ Hughes Satellite Codes Spark Caltech Patent Suit.[2]

## 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.