computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

, repeat-accumulate codes (RA codes) are a low complexity class of

error-correcting code In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The centra ...

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 Information is an abstract concept that refers to something which has the power to inform. At the most fundamental level, it pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natur ...

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 Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in m ...

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

x_i = x_+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 build on top of the ideas of RA codes. IRA replaces the outer code in RA code with a low density generator matrix code. IRA codes first repeats information bits different times, and then accumulates subsets of these repeated bits to generate parity bits. The irregular degree profile on the information nodes, together with the degree profile on the check nodes, can be designed using density evolution. Systematic IRA codes are considered a form of

LDPC Low-density parity-check (LDPC) codes are a class of error correction codes which (together with the closely-related turbo codes) have gained prominence in coding theory and information theory since the late 1990s. The codes today are widely ...

code. Litigation over whether the DVB-S2 LDPC code is a form of IRA code is ongoing.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.

Notes

References

* {{cite conference , first1=D. , last1=Divsalar , first2=H. , last2=Jin , first3=R.J. , last3=McEliece , title=Coding theorems for 'turbo-like' codes , book-title=Proceedings of the annual Allerton Conference on Communication control and Computing , date=September 1998 , pages=201–210 , volume=36 , publisher=University Of Illinois , url=https://www.researchgate.net/publication/243768674

External links

Iterative Error Correction: Turbo, Low-Density Parity-Check, and Repeat-Accumulate Codes
Error detection and correction