Irregular LDPC code

Irregular LDPC code[1,2]

Description

An LDPC code whose parity-check matrix has a variable number of entries in each row or column.

Rate

Nearly achieve capacity against binary-input additive Gaussian white noise using iterative decoding [3,4]. Such sequences have sublinearly growing distance per block length [5].

Realizations

Satellite communication after concatenating with a modulation scheme [6].

Notes

Useful tools for designing irregular LDPC codes can be found in Refs. [7,8].

Cousin

Regular LDPC code— Irregular LDPC codes have variable node and check node degrees, while regular LDPC codes have fixed node degrees. Irregular LDPC codes with optimized degree distributions can outperform regular ones under iterative decoding [9,10].

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

Parents

Multi-edge LDPC code

The multi-edge code construction generalizes several of the original examples of irregular LDPC codes. Irregular LDPC codes can be formulated as multi-edge LDPC codes [11; Sec. XI].

Irregular LDPC code

Children

Accumulate-repeat-accumulate (ARA) code

Extended IRA (eIRA) code

Block LDPC (B-LDPC) code

References

[1]: M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs”, IEEE Transactions on Information Theory 47, 585 (2001) DOI
[2]: M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, D. A. Spielman, and V. Stemann, “Practical loss-resilient codes”, Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC ’97 150 (1997) DOI
[3]: T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes”, IEEE Transactions on Information Theory 47, 619 (2001) DOI
[4]: Sae-Young Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit”, IEEE Communications Letters 5, 58 (2001) DOI
[5]: C. Di, T. J. Richardson, and R. L. Urbanke, “Weight Distribution of Low-Density Parity-Check Codes”, IEEE Transactions on Information Theory 52, 4839 (2006) DOI
[6]: S. ten Brink, G. Kramer, and A. Ashikhmin, “Design of Low-Density Parity-Check Codes for Modulation and Detection”, IEEE Transactions on Communications 52, 670 (2004) DOI
[7]: Sae-Young Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation”, IEEE Transactions on Information Theory 47, 657 (2001) DOI
[8]: R. Urbanke, LdpcOpt - a fast and accurate degree distribution optimizer for LDPC code ensembles (2001).
[9]: D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices”, IEEE Transactions on Information Theory 45, 399 (1999) DOI
[10]: T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding”, IEEE Transactions on Information Theory 47, 599 (2001) DOI
[11]: Richardson, Tom, and Rüdiger Urbanke. “Multi-edge type LDPC codes.” Workshop honoring Prof. Bob McEliece on his 60th birthday, California Institute of Technology, Pasadena, California. 2002.

Page edit log

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

Cite as:

“Irregular LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/irregular_ldpc

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