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 [1]. Puncturing lessens the decoding complexity while still allowing sequences of codes to achieve capacity [5].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 accumulator to obtain \begin{align} (u_{1},u_{1}+u_{2},\cdots,u_{1}+\cdots+u_{N})~, \tag*{(1)}\end{align} where \(N\) is the length of the permuted LDGM output.Decoding
Linear-time decoder [1].Realizations
LDPC codes are used for digital satellite video broadcasting per the DVB-S2 standard [6,7] 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].Cousins
- Low-density generator-matrix (LDGM) code— IRA codes replace the outer 1-in-3 repetition encoding step in RA codes with an LDGM code.
- MacKay-Neal LDPC (MN-LDPC) code— MN-LDPC and IRA codes intersect for certain parameters [8].
Primary Hierarchy
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Parents
Protograph LDPC code\(q\)-ary LDPC Tanner Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) LRC Distributed-storage ECC
IRA codes can be formulated as protograph LDPC codes [9].
IRA codes can be interpreted as serial concatenated codes [10].
Irregular repeat-accumulate (IRA) code
Children
IRA codes for which the outer code is a 1-in-3 repetition code reduce to RA codes.
References
- [1]
- H. Jin, A. Khandekar, and R. J. 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]
- H. Jin, A. Khandekar, and R. J. McEliece, SERIAL CONCATENATION OF INTERLEAVED CONVOLUTIONAL CODES FORMING TURBO-LIKE CODES. United States Patent Number 7116710B1 (2023).
- [4]
- A. Roumy, S. Guemghar, G. Caire, and S. Verdu, “Design Methods for Irregular Repeat–Accumulate Codes”, IEEE Transactions on Information Theory 50, 1711 (2004) DOI
- [5]
- 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
- [6]
- 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
- [7]
- 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.
- [8]
- H. D. Pfister, private communication, 2022.
- [9]
- 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
- [10]
- S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, “Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding”, IEEE Transactions on Information Theory 44, 909 (1998) DOI
Page edit log
- Victor V. Albert (2023-05-04) — most recent
Cite as:
“Irregular repeat-accumulate (IRA) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ira