Accumulate-repeat-accumulate (ARA) code

Accumulate-repeat-accumulate (ARA) code[1]

Description

A generalization of the RA code in which the outer repetition-code encoding step is augmented with an acumulator acting on a fraction of the incoming bits. In addition, the code may be punctured after the final acumulating step.

Member of code lists

Primary Hierarchy

Classical Domain

Binary Kingdom

Binary codeECC

Binary group-orbit codeECC

Linear binary codeLinear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC

Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC

Multi-edge LDPC code

Irregular LDPC code

Parents

Irregular LDPC code

Protograph LDPC code\(q\)-ary LDPC Tanner Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) LRC Distributed-storage ECC

ARA codes can be formulated as protograph LDPC codes [2].

Accumulate-repeat-accumulate (ARA) code

Children

Repeat-accumulate (RA) code

ARA codes with no pre-encoding acumulator and no post-acumulator puncturing reduce to RA codes.

References

[1]: A. Abbasfar, D. Divsalar, and K. Yao, “Accumulate-Repeat-Accumulate Codes”, IEEE Transactions on Communications 55, 692 (2007) DOI
[2]: D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size”, GLOBECOM ’05. IEEE Global Telecommunications Conference, 2005. 5 pp. (2005) DOI

Page edit log

Victor V. Albert (2023-05-04) — most recent

Cite as:

“Accumulate-repeat-accumulate (ARA) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ara

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/tanner/irregular/ra/ara.yml.