Low-Density Parity-Check Codes Celebrating Receipt of Japan Prize by Prof. Robert G. Gallager
Robert G. Gallager, Professor Emeritus at Massachusetts Institute of Technology, was awarded the 2020 Japan Prize. The low-density parity-check code (LDPC code), the award's subject, is an error correction code proposed by Professor, Gallager in his doctoral thesis in 1960. It has now become an...
Saved in:
| Published in | Denshi Jouhou Tsuushin Gakkai Kiso, Kyoukai Sosaieti fundamentals review Vol. 14; no. 3; pp. 217 - 228 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | Japanese |
| Published |
Tokyo
The Institute of Electronics, Information and Communication Engineers
01.01.2021
Japan Science and Technology Agency |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1882-0875 |
| DOI | 10.1587/essfr.14.3_217 |
Cover
| Abstract | Robert G. Gallager, Professor Emeritus at Massachusetts Institute of Technology, was awarded the 2020 Japan Prize. The low-density parity-check code (LDPC code), the award's subject, is an error correction code proposed by Professor, Gallager in his doctoral thesis in 1960. It has now become an essential fundamental technology that supports our modern digital life. In this article, we describe the LDPC codes that can derive the optimal decoding algorithm in probabilistic inference. Furthermore, in this article we also introduce a practical LDPC code construction. |
|---|---|
| AbstractList | Robert G. Gallager, Professor Emeritus at Massachusetts Institute of Technology, was awarded the 2020 Japan Prize. The low-density parity-check code (LDPC code), the award's subject, is an error correction code proposed by Professor, Gallager in his doctoral thesis in 1960. It has now become an essential fundamental technology that supports our modern digital life. In this article, we describe the LDPC codes that can derive the optimal decoding algorithm in probabilistic inference. Furthermore, in this article we also introduce a practical LDPC code construction. |
| Author | UCHIKAWA, Hironori |
| Author_xml | – sequence: 1 fullname: UCHIKAWA, Hironori organization: Institute of Memory Technology R&D, Kioxia Corporation |
| BookMark | eNo9j0tPwzAQhC0EEqX0yhFV4uzi9aPenBAKTykSHHq37GRDE0pS7FSo_55AEXPYOcynHc0ZO-76jhi7ALEAg_aaUqrjAvRCOQn2iE0AUXKB1pyyWUqtGLUUSlicsMui_-J31KVm2M9ffRyN52sq3-d5X1E6Zye13ySa_fmUrR7uV_kTL14en_PbgreokXs0dRV0IOmroFSmvBHaeALwqDISEkStRQ0ogwzLGkwmLSKUVSAV9MhP2dXh7Tb2nztKg2v7XezGRie11cZCJnGkbg5Umwb_Rm4bmw8f987HoSk35H53O9BO_Zxx-n9Srn101KlvgFRV9Q |
| ContentType | Journal Article |
| Copyright | 2021 The Institute of Electronics, Information and Communication Engineers Copyright Japan Science and Technology Agency 2020 |
| Copyright_xml | – notice: 2021 The Institute of Electronics, Information and Communication Engineers – notice: Copyright Japan Science and Technology Agency 2020 |
| DBID | 7SP 8FD L7M |
| DOI | 10.1587/essfr.14.3_217 |
| DatabaseName | Electronics & Communications Abstracts Technology Research Database Advanced Technologies Database with Aerospace |
| DatabaseTitle | Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1882-0875 |
| EndPage | 228 |
| ExternalDocumentID | article_essfr_14_3_14_217_article_char_en |
| GroupedDBID | ABJNI ACGFS ALMA_UNASSIGNED_HOLDINGS JSF KQ8 OK1 RJT 7SP 8FD L7M |
| ID | FETCH-LOGICAL-j848-a85fdb4be2adb3393a5045ae11a839e0210f40f182b2b6f15927881cdbe3b4393 |
| IngestDate | Mon Jun 30 06:46:06 EDT 2025 Wed Sep 03 06:31:07 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Issue | 3 |
| Language | Japanese |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-j848-a85fdb4be2adb3393a5045ae11a839e0210f40f182b2b6f15927881cdbe3b4393 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://www.jstage.jst.go.jp/article/essfr/14/3/14_217/_article/-char/en |
| PQID | 2474571928 |
| PQPubID | 2048427 |
| PageCount | 12 |
| ParticipantIDs | proquest_journals_2474571928 jstage_primary_article_essfr_14_3_14_217_article_char_en |
| PublicationCentury | 2000 |
| PublicationDate | 2021/01/01 |
| PublicationDateYYYYMMDD | 2021-01-01 |
| PublicationDate_xml | – month: 01 year: 2021 text: 2021/01/01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Tokyo |
| PublicationPlace_xml | – name: Tokyo |
| PublicationTitle | Denshi Jouhou Tsuushin Gakkai Kiso, Kyoukai Sosaieti fundamentals review |
| PublicationTitleAlternate | IEICE Fundamentals Review |
| PublicationYear | 2021 |
| Publisher | The Institute of Electronics, Information and Communication Engineers Japan Science and Technology Agency |
| Publisher_xml | – name: The Institute of Electronics, Information and Communication Engineers – name: Japan Science and Technology Agency |
| References | 24) T.J. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, 2008. 17) A.K. Pradhan, A. Subramanian, and A. Thangaraj, “Deterministic constructions for large girth protograph LDPC codes,” IEEE International Symposium on Information Theory (ISIT), pp. 1680-1684, July 2013. 19) R. Smarandache and P.O. Vontobel, “Quasi-cyclic LDPC codes: Influence of proto- and Tanner-graph structure on minimum hamming distance upper bounds,” IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 585-607, Feb. 2012. 3) R.G. Gallager, Low-Density Parity-Check Codes, MIT Press, 1963. 18) M.P.C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1788-1793, 2004. 22) T.J. Richardson, “Error floors of LDPC codes,” 41st Annual Allerton Conference on Communications, pp. 1426-1435, 2003. 23) S. Lin and D.J. Costello, Error Control Coding, 2 edition, Prentice Hall, 2004. 14) T.J. Richardson and R. Urbanke, “Multi-edge type LDPC codes,” 2004. https://www.researchgate.net/publication/37439748_Multi-edge_type_LDPC_codes 10) J. Thorpe, “Low density parity check (LDPC) codes constructed from protographs,” JPL IPN Progress Report, 42-154, pp. 1-7, Aug. 2003. 6) T.J. Richardson, M. Shokrollahi, and R. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 619-637, 2001. 12) Y. Fang, G. Bi, Y.L. Guan, and F.C.M. Lau, “A survey on protograph LDPC codes and their applications,” IEEE Commun. Surveys Tuts., vol. 17, no. 4, pp. 1989-2016, 2015. 2) C.E. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, vol. 27, no. 3, pp. 379-423, 1948. 20) D.M. Arnold, E. Eleftheriou, and X.Y. Hu, “Progressive edge-growth Tanner graphs,” IEEE Global Telecommunications Conference (GLOBECOM), vol. 2, pp. 995-1001, 2001. 13) D. Divsalar, S. Dolinar, C.R. Jones, and K. Andrews, “Capacity-approaching protograph codes,” IEEE J. Sel. Areas Commun., vol. 27, no. 6, pp. 876-888, 2009. 1) 萩原学（編著），進化する符号理論，日本評論社，2016. 25) W.E. Ryan and S. Lin, Channel Codes: Classical and Modern, Cambridge University Press, 2009. 8) 笠原正雄，“リード・ソロモン符号の半世紀，” 信学FR誌，vol. 5, no. 1, pp. 28-41, 2011. 7) R. Gallager, “A simple derivation of the coding theorem and some applications,” IEEE Trans. Inf. Theory, vol. 11, no. 1, pp. 3-18, Jan. 1965. 5) T.J. Richardson and R. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 599-618, 2001. 26) 笠井健太，“多元LDPC符号とその応用，” 信学技報，vol. 110, no. 205, pp. 1-6, Sept. 2010. 21) T. Tian, C. Jones, J. Villasenor, and R.D. Wesel, “Selective avoidance of cycles in irregular LDPC code construction,” IEEE Trans. Commun., vol. 52, no. 8, pp. 1242-1247, 2004. 9) “Robert G. Gallager Wins the 1999 Harvey Prize.” https://wayback.archive-it.org/all/20070417175505/ http://www.ee.ucla.edu/~congshen/robert_gallager.pdf 15) T.V. Nguyen, A. Nosratinia, and D. Divsalar, “The design of rate-compatible protograph LDPC codes,” IEEE Trans. Commun., vol. 60, no. 10, pp. 2841-2850, 2012. 16) H. Uchikawa, “Design of non-precoded protograph-based LDPC codes,” IEEE International Symposium on Information Theory (ISIT), pp. 2779-2783, June 2014. 27) 笠井健太，“空間結合符号とその応用，” 信学技報，vol. 111, no. 220, pp. 1-8, Sept. 2011. 4) D.J.C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399-431, March 1999. 11) G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” IEEE Global Telecommunications Conference (GLOBECOM), pp. 3250-3254, Nov. 2007. |
| References_xml | – reference: 26) 笠井健太，“多元LDPC符号とその応用，” 信学技報，vol. 110, no. 205, pp. 1-6, Sept. 2010. – reference: 11) G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” IEEE Global Telecommunications Conference (GLOBECOM), pp. 3250-3254, Nov. 2007. – reference: 13) D. Divsalar, S. Dolinar, C.R. Jones, and K. Andrews, “Capacity-approaching protograph codes,” IEEE J. Sel. Areas Commun., vol. 27, no. 6, pp. 876-888, 2009. – reference: 18) M.P.C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1788-1793, 2004. – reference: 27) 笠井健太，“空間結合符号とその応用，” 信学技報，vol. 111, no. 220, pp. 1-8, Sept. 2011. – reference: 6) T.J. Richardson, M. Shokrollahi, and R. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 619-637, 2001. – reference: 8) 笠原正雄，“リード・ソロモン符号の半世紀，” 信学FR誌，vol. 5, no. 1, pp. 28-41, 2011. – reference: 14) T.J. Richardson and R. Urbanke, “Multi-edge type LDPC codes,” 2004. https://www.researchgate.net/publication/37439748_Multi-edge_type_LDPC_codes – reference: 9) “Robert G. Gallager Wins the 1999 Harvey Prize.” https://wayback.archive-it.org/all/20070417175505/ http://www.ee.ucla.edu/~congshen/robert_gallager.pdf – reference: 16) H. Uchikawa, “Design of non-precoded protograph-based LDPC codes,” IEEE International Symposium on Information Theory (ISIT), pp. 2779-2783, June 2014. – reference: 21) T. Tian, C. Jones, J. Villasenor, and R.D. Wesel, “Selective avoidance of cycles in irregular LDPC code construction,” IEEE Trans. Commun., vol. 52, no. 8, pp. 1242-1247, 2004. – reference: 1) 萩原学（編著），進化する符号理論，日本評論社，2016. – reference: 12) Y. Fang, G. Bi, Y.L. Guan, and F.C.M. Lau, “A survey on protograph LDPC codes and their applications,” IEEE Commun. Surveys Tuts., vol. 17, no. 4, pp. 1989-2016, 2015. – reference: 25) W.E. Ryan and S. Lin, Channel Codes: Classical and Modern, Cambridge University Press, 2009. – reference: 22) T.J. Richardson, “Error floors of LDPC codes,” 41st Annual Allerton Conference on Communications, pp. 1426-1435, 2003. – reference: 3) R.G. Gallager, Low-Density Parity-Check Codes, MIT Press, 1963. – reference: 2) C.E. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, vol. 27, no. 3, pp. 379-423, 1948. – reference: 17) A.K. Pradhan, A. Subramanian, and A. Thangaraj, “Deterministic constructions for large girth protograph LDPC codes,” IEEE International Symposium on Information Theory (ISIT), pp. 1680-1684, July 2013. – reference: 19) R. Smarandache and P.O. Vontobel, “Quasi-cyclic LDPC codes: Influence of proto- and Tanner-graph structure on minimum hamming distance upper bounds,” IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 585-607, Feb. 2012. – reference: 7) R. Gallager, “A simple derivation of the coding theorem and some applications,” IEEE Trans. Inf. Theory, vol. 11, no. 1, pp. 3-18, Jan. 1965. – reference: 10) J. Thorpe, “Low density parity check (LDPC) codes constructed from protographs,” JPL IPN Progress Report, 42-154, pp. 1-7, Aug. 2003. – reference: 23) S. Lin and D.J. Costello, Error Control Coding, 2 edition, Prentice Hall, 2004. – reference: 4) D.J.C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399-431, March 1999. – reference: 15) T.V. Nguyen, A. Nosratinia, and D. Divsalar, “The design of rate-compatible protograph LDPC codes,” IEEE Trans. Commun., vol. 60, no. 10, pp. 2841-2850, 2012. – reference: 5) T.J. Richardson and R. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 599-618, 2001. – reference: 20) D.M. Arnold, E. Eleftheriou, and X.Y. Hu, “Progressive edge-growth Tanner graphs,” IEEE Global Telecommunications Conference (GLOBECOM), vol. 2, pp. 995-1001, 2001. – reference: 24) T.J. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, 2008. |
| SSID | ssj0000603078 ssib005296245 ssib005492307 |
| Score | 1.8447651 |
| Snippet | Robert G. Gallager, Professor Emeritus at Massachusetts Institute of Technology, was awarded the 2020 Japan Prize. The low-density parity-check code (LDPC... |
| SourceID | proquest jstage |
| SourceType | Aggregation Database Publisher |
| StartPage | 217 |
| SubjectTerms | Algorithms Awards & honors Binary system Codes Decoding Density Differential evolution Error correcting codes Error correction LDPC codes Low density parity check codes Maximum a posteriori decoding Parity Probabilistic inference Protograph Quasi-cyclic LDPC codes Sum-product decoding |
| Subtitle | Celebrating Receipt of Japan Prize by Prof. Robert G. Gallager |
| Title | Low-Density Parity-Check Codes |
| URI | https://www.jstage.jst.go.jp/article/essfr/14/3/14_217/_article/-char/en https://www.proquest.com/docview/2474571928 |
| Volume | 14 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| ispartofPNX | IEICE ESS Fundamentals Review, 2021/01/01, Vol.14(3), pp.217-228 |
| journalDatabaseRights | – providerCode: PRVAFT databaseName: Open Access Digital Library databaseCode: KQ8 dateStart: 20070101 customDbUrl: isFulltext: true eissn: 1882-0875 dateEnd: 99991231 titleUrlDefault: http://grweb.coalliance.org/oadl/oadl.html omitProxy: true ssIdentifier: ssj0000603078 providerName: Colorado Alliance of Research Libraries |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PT9swFLY2dmEHxAZo_Kp62A0ZGttJnGNVWrXrhoRUBLfITmxGJ7VTKULir-c9xwSn3YFxiao0jVy_58_fs_29R8h3abLIltrQQvCCikhbmqkioTxLhJEdlSYlaod_XSTDK_HjJr55rbHp1CVLfVo8_VNX8h6rwj2wK6pk_8Oy9UvhBnwG-8IVLAzXN9n45_yRnuMJdNT5KSxDR3u_TfEHRnnpzwZ63jnqj3r9E6yvMUDpR5XR_35lZ-CqNxyNu9ddNx2h_G2-uAtXBVi0sirgStSHpw36dVEdDz61NtJtUjTUKHUqRJ8uvUJGpOKY_r4BnSJwEd7AwTSYUlml_15D6xjXOwaA6HYBiH3K8_pnjQzYvn9z9yDEKjnHCzybv3yDCjVwiI_kEwNwxwoe48sgSxnLEhZsnrqkdD7qrSZsRDrpU3pCo86aTQJyMgWqfrs-XzsSMtkmWz56aHerBn0hH6bqK_kc5JTcIa3AKdqhU7SdU-ySyaA_6Q2pL4JBp1JIqmQMQ0low1SpOc-4ioGEKxNFCqitwYjdio6FKFEznVggpwwLBBQw_LgGssn3yMZsPjPfSDs10jDLOhZIuYBu0pG1QEY7HGC8yMpon8jqb-Z_q0Qn-Zs7fp8cvXRM7sfHfc5EKuIUIgh58P43H5LNV_c-IhvLxYM5Bhq41C1n5Gfk5GGq |
| linkProvider | Colorado Alliance of Research Libraries |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Low-Density+Parity-Check+Codes&rft.jtitle=IEICE+ESS+Fundamentals+Review&rft.au=UCHIKAWA%2C+Hironori&rft.date=2021-01-01&rft.pub=The+Institute+of+Electronics%2C+Information+and+Communication+Engineers&rft.eissn=1882-0875&rft.volume=14&rft.issue=3&rft.spage=217&rft.epage=228&rft_id=info:doi/10.1587%2Fessfr.14.3_217&rft.externalDocID=article_essfr_14_3_14_217_article_char_en |