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

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

error-correcting code In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...

s. They were devised so that their

ensemble weight distributions Ensemble may refer to: Art * Architectural ensemble * ''Ensemble'' (album), Kendji Girac 2015 album * Ensemble (band), a project of Olivier Alary * Ensemble cast (drama, comedy) * Ensemble (musical theatre), also known as the chorus * ''Ensem ...

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 that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random, ...

of length

is repeated

times, scrambled by an

interleaver In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...

of size

, and then encoded by a rate 1 accumulator. The accumulator can be viewed as a truncated rate 1

recursive Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ...

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 In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel. An LDPC code is constructed using a sparse Tanner graph (subclass of the bip ...

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

{{reflist

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

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