Irregular repeat-accumulate (IRA) code[13] 

Description

A generalization of the RA code in which the outer 1-in-3 repetition encoding step is replaced by an LDGM code. A simple version is when different bits in the RA block are repeated a different number of times.

IRA codes can be optimized against various noise channels [4].

Rate

IRA codes nearly achieve the Shannon capacity of the binary erasure channel using iterative decoding [5]. Puncturing ressens the decoding complexity while still allowing sequences of codes to achive capacity [6].

Encoding

One linear-time encoder for a systematic IRA code consists of first encoding into an \([n,k]\) LDGM binary linear code, applying a random permutation, and then applying an acumulator to obtain \begin{align} (u_{1},u_{1}+u_{2},\cdots,u_{1}+\cdots+u_{3K})~. \tag*{(1)}\end{align}

Decoding

Linear-time decoder [5].

Realizations

LDPC codes are used for digital satellite video broadcasting per the DVB-S2 standard [7,8] utilize IRA code features and are subject to ongoing litigation; see Ref. [3].Apple and Broadcom Wi-Fi devices utilize IRA encoding and decoding code features and are subject to ongoing litigation; see Ref. [3].

Parents

Child

Cousins

References

[1]
Hui Jin, Aamod Khandekar, and Robert McEliece. "Irregular repeat-accumulate codes." Proc. 2nd Int. Symp. Turbo codes and related topics. 2000.
[2]
A. D. Khandekar, Graph-Based Codes and Iterative Decoding, California Institute of Technology, 2003 DOI
[3]
Hui Jin, Aamod Khandekar, and Robert J. McEliece. "Serial concatenation of interleaved convolutional codes forming turbo-like codes." United States Patent Number 7116710B1 (2023).
[4]
A. Roumy et al., “Design Methods for Irregular Repeat–Accumulate Codes”, IEEE Transactions on Information Theory 50, 1711 (2004) DOI
[5]
Jin, Hui, Aamod Khandekar, and Robert McEliece. "Irregular repeat-accumulate codes." Proc. 2nd Int. Symp. Turbo codes and related topics. 2000.
[6]
H. D. Pfister, I. Sason, and R. Urbanke, “Capacity-Achieving Ensembles for the Binary Erasure Channel With Bounded Complexity”, IEEE Transactions on Information Theory 51, 2352 (2005) DOI
[7]
R. Purnamasari, H. Wijanto, and I. Hidayat, “Design and implementation of LDPC(Low Density Parity Check) coding technique on FPGA (Field Programmable Gate Array) for DVB-S2 (Digital Video Broadcasting-Satellite)”, 2014 IEEE International Conference on Aerospace Electronics and Remote Sensing Technology 83 (2014) DOI
[8]
ETSI, ETSI. "Digital video broadcasting (dvb); second generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications." Part II: S2-Extensions (DVB-S2X) (2005): 22-27.
[9]
D. Divsalar et al., “Protograph based LDPC codes with minimum distance linearly growing with block size”, GLOBECOM ’05. IEEE Global Telecommunications Conference, 2005. (2005) DOI
[10]
S. Benedetto et al., “Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding”, IEEE Transactions on Information Theory 44, 909 (1998) DOI
[11]
Henry D. Pfister, private communication, 2022
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: ira

Cite as:
“Irregular repeat-accumulate (IRA) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ira
BibTeX:
@incollection{eczoo_ira, title={Irregular repeat-accumulate (IRA) code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/ira} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/ira

Cite as:

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

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