Low-Complexity Chase Decoding of Hermitian Codes With Improved Interpolation and Root-Finding
This paper proposes the low-complexity Chase (LCC) decoding for Hermitian codes, which is facilitated by both the improved interpolation and root-finding. By identifying <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula> unreliable receive...
Saved in:
| Published in: | IEEE transactions on communications Vol. 73; no. 8; pp. 5509 - 5522 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
IEEE
01.08.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects: | |
| ISSN: | 0090-6778, 1558-0857 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | This paper proposes the low-complexity Chase (LCC) decoding for Hermitian codes, which is facilitated by both the improved interpolation and root-finding. By identifying <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula> unreliable received symbols, <inline-formula> <tex-math notation="LaTeX">2^{\eta } </tex-math></inline-formula> test-vectors are formulated, each of which is decoded by the interpolation based Guruswami-Sudan (GS) algorithm. To reduce both the interpolation complexity and latency, the re-encoding transform (ReT) is introduced through defining the Lagrange interpolation polynomials over the Hermitian function fields. The interpolation polynomial is further computed through module basis reduction (BR) that yields the Gröbner basis that contains the desired polynomial. The BR interpolation exhibits a greater parallelism than the conventional Kötter's interpolation. Moreover, the <inline-formula> <tex-math notation="LaTeX">2^{\eta } </tex-math></inline-formula> root-finding processes are facilitated by estimating the codewords directly from the interpolation outcomes. It eliminates the re-encoding computation for identifying the most likely candidate from the decoding output list. It is also shown that the average LCC decoding complexity can be further reduced by both assessing the re-encoding outcome and decoding the test-vectors progressively. They can achieve an early decoding termination once a codeword that satisfies the maximum likelihood (ML) criterion is found. Our simulation results demonstrate that the decoding complexity and latency can be significantly reduced over the existing decoding algorithms. |
|---|---|
| AbstractList | This paper proposes the low-complexity Chase (LCC) decoding for Hermitian codes, which is facilitated by both the improved interpolation and root-finding. By identifying <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula> unreliable received symbols, <inline-formula> <tex-math notation="LaTeX">2^{\eta } </tex-math></inline-formula> test-vectors are formulated, each of which is decoded by the interpolation based Guruswami-Sudan (GS) algorithm. To reduce both the interpolation complexity and latency, the re-encoding transform (ReT) is introduced through defining the Lagrange interpolation polynomials over the Hermitian function fields. The interpolation polynomial is further computed through module basis reduction (BR) that yields the Gröbner basis that contains the desired polynomial. The BR interpolation exhibits a greater parallelism than the conventional Kötter's interpolation. Moreover, the <inline-formula> <tex-math notation="LaTeX">2^{\eta } </tex-math></inline-formula> root-finding processes are facilitated by estimating the codewords directly from the interpolation outcomes. It eliminates the re-encoding computation for identifying the most likely candidate from the decoding output list. It is also shown that the average LCC decoding complexity can be further reduced by both assessing the re-encoding outcome and decoding the test-vectors progressively. They can achieve an early decoding termination once a codeword that satisfies the maximum likelihood (ML) criterion is found. Our simulation results demonstrate that the decoding complexity and latency can be significantly reduced over the existing decoding algorithms. This paper proposes the low-complexity Chase (LCC) decoding for Hermitian codes, which is facilitated by both the improved interpolation and root-finding. By identifying [Formula Omitted] unreliable received symbols, [Formula Omitted] test-vectors are formulated, each of which is decoded by the interpolation based Guruswami-Sudan (GS) algorithm. To reduce both the interpolation complexity and latency, the re-encoding transform (ReT) is introduced through defining the Lagrange interpolation polynomials over the Hermitian function fields. The interpolation polynomial is further computed through module basis reduction (BR) that yields the Gröbner basis that contains the desired polynomial. The BR interpolation exhibits a greater parallelism than the conventional Kötter’s interpolation. Moreover, the [Formula Omitted] root-finding processes are facilitated by estimating the codewords directly from the interpolation outcomes. It eliminates the re-encoding computation for identifying the most likely candidate from the decoding output list. It is also shown that the average LCC decoding complexity can be further reduced by both assessing the re-encoding outcome and decoding the test-vectors progressively. They can achieve an early decoding termination once a codeword that satisfies the maximum likelihood (ML) criterion is found. Our simulation results demonstrate that the decoding complexity and latency can be significantly reduced over the existing decoding algorithms. |
| Author | Zhao, Jianguo Chen, Li Liang, Jiwei |
| Author_xml | – sequence: 1 givenname: Jiwei surname: Liang fullname: Liang, Jiwei email: liangjw59@mail2.sysu.edu.cn organization: School of System Science and Engineering, Sun Yat-sen University, Guangzhou, China – sequence: 2 givenname: Jianguo surname: Zhao fullname: Zhao, Jianguo email: zhaojg5@mail2.sysu.edu.cn organization: School of System Science and Engineering, Sun Yat-sen University, Guangzhou, China – sequence: 3 givenname: Li orcidid: 0000-0002-1725-1901 surname: Chen fullname: Chen, Li email: chenli55@mail.sysu.edu.cn organization: School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China |
| BookMark | eNpNkMtKw0AUhgepYFt9AXEx4Dr1zC2XpURrCy0FqbiSIU1O7JRmpmZStW_v1LoQDpzN_53LNyA96ywScs1gxBhkd8t8MZ-POHA5EopLEOqM9JlSaQSpSnqkD5BBFCdJekEG3m8AIIREn7zN3FeUu2a3xW_THWi-LjzSByxdZew7dTWdYNuYzhSW5q5CT19Nt6bTZte6T6zo1HbY7ty26IyztLAVfXaui8bGHvlLcl4XW49Xf31IXsaPy3wSzRZP0_x-FpVcJl0kMGarpFIMKqi5KFFUSslY1jIDVFAhIK4ynqQ1lEWtQql6JUSRMUCO4ZEhuT3NDVd97NF3euP2rQ0rteAyVjEEFyHFT6mydd63WOtda5qiPWgG-qhR_2rUR436T2OAbk6QQcR_QMpSxaT4AVCrcKM |
| CODEN | IECMBT |
| Cites_doi | 10.1109/TIT.1969.1054260 10.1109/TIT.2012.2188274 10.1109/TIT.2022.3188843 10.1109/18.312155 10.1109/TCOMM.2009.08.070302 10.1109/18.476240 10.1109/18.720550 10.1109/TCOMM.2017.2786667 10.1016/j.jsc.2007.12.004 10.1109/TIT.2010.2096034 10.1109/TIT.2021.3109447 10.1016/j.jsc.2008.01.002 10.1049/iet-com.2015.0873 10.1007/978-3-540-76878-4 10.1109/ICC.2007.145 10.1109/18.945273 10.1109/tit.2025.3550750 10.1109/TIT.2015.2424415 10.1109/TIT.2003.819332 10.1109/GCWkshps58843.2023.10464872 10.1016/S0747-7171(02)00139-6 10.1109/ISCAS.2009.5118353 10.1109/18.782097 10.1007/3-540-46796-3_26 10.1109/18.817522 10.1109/TIT.2010.2046208 10.1109/TIT.2020.3042248 10.1109/TCOMM.2020.3011991 10.1109/TIT.2009.2039073 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2025 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2025 |
| DBID | 97E RIA RIE AAYXX CITATION 7SP 8FD L7M |
| DOI | 10.1109/TCOMM.2024.3524035 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005-present IEEE All-Society Periodicals Package (ASPP) 1998-Present IEEE Electronic Library (IEL) CrossRef Electronics & Communications Abstracts Technology Research Database Advanced Technologies Database with Aerospace |
| DatabaseTitle | CrossRef Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts |
| DatabaseTitleList | Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1558-0857 |
| EndPage | 5522 |
| ExternalDocumentID | 10_1109_TCOMM_2024_3524035 10818514 |
| Genre | orig-research |
| GrantInformation_xml | – fundername: Natural Science Foundation of Guangdong Province grantid: 2024A1515010213 funderid: 10.13039/501100003453 – fundername: National Natural Science Foundation of China (NSFC) grantid: 62071498 funderid: 10.13039/501100001809 |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 85S 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACIWK ACKIV ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD HZ~ H~9 IAAWW IBMZZ ICLAB IES IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P RIA RIE RNS TAE TN5 VH1 ZCA ZCG AAYXX CITATION 7SP 8FD L7M |
| ID | FETCH-LOGICAL-c247t-3e61b7d510d0f23ce3d55464f490e50de0eeb9278f0caf5af55fb33a910e2e403 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001551629100022&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0090-6778 |
| IngestDate | Sat Nov 01 14:55:13 EDT 2025 Sat Nov 29 07:36:34 EST 2025 Wed Aug 27 07:40:15 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 8 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c247t-3e61b7d510d0f23ce3d55464f490e50de0eeb9278f0caf5af55fb33a910e2e403 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-1725-1901 |
| PQID | 3246560155 |
| PQPubID | 85472 |
| PageCount | 14 |
| ParticipantIDs | crossref_primary_10_1109_TCOMM_2024_3524035 ieee_primary_10818514 proquest_journals_3246560155 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-08-01 |
| PublicationDateYYYYMMDD | 2025-08-01 |
| PublicationDate_xml | – month: 08 year: 2025 text: 2025-08-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on communications |
| PublicationTitleAbbrev | TCOMM |
| PublicationYear | 2025 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | Kötter (ref8) 1996 ref13 ref12 ref15 ref14 ref31 ref30 ref11 ref33 ref10 ref32 ref2 ref17 ref16 ref19 ref18 Nielsen (ref29) 2001 Goppa (ref1) 1977; 13 Chen (ref21) ref24 ref23 ref26 ref25 ref20 ref22 ref28 ref27 ref7 ref9 ref4 ref3 ref6 ref5 |
| References_xml | – ident: ref2 doi: 10.1109/TIT.1969.1054260 – ident: ref25 doi: 10.1109/TIT.2012.2188274 – ident: ref12 doi: 10.1109/TIT.2022.3188843 – ident: ref24 doi: 10.1109/18.312155 – ident: ref17 doi: 10.1109/TCOMM.2009.08.070302 – ident: ref3 doi: 10.1109/18.476240 – ident: ref28 doi: 10.1109/18.720550 – ident: ref20 doi: 10.1109/TCOMM.2017.2786667 – ident: ref10 doi: 10.1016/j.jsc.2007.12.004 – ident: ref14 doi: 10.1109/TIT.2010.2096034 – ident: ref15 doi: 10.1109/TIT.2021.3109447 – ident: ref9 doi: 10.1016/j.jsc.2008.01.002 – ident: ref26 doi: 10.1049/iet-com.2015.0873 – ident: ref30 doi: 10.1007/978-3-540-76878-4 – ident: ref7 doi: 10.1109/ICC.2007.145 – ident: ref6 doi: 10.1109/18.945273 – year: 1996 ident: ref8 article-title: On algebraic decoding of algebraic-geometric and cyclic codes – ident: ref13 doi: 10.1109/tit.2025.3550750 – ident: ref11 doi: 10.1109/TIT.2015.2424415 – volume: 13 start-page: 33 issue: 1 year: 1977 ident: ref1 article-title: Codes associated with divisors publication-title: Problemy Peredachi Informatsii – ident: ref16 doi: 10.1109/TIT.2003.819332 – ident: ref23 doi: 10.1109/GCWkshps58843.2023.10464872 – ident: ref32 doi: 10.1016/S0747-7171(02)00139-6 – ident: ref22 doi: 10.1109/ISCAS.2009.5118353 – ident: ref4 doi: 10.1109/18.782097 – ident: ref31 doi: 10.1007/3-540-46796-3_26 – start-page: 180 volume-title: Proc. IEEE Int. Symp. Inf. Theory (ISIT) ident: ref21 article-title: Algebraic chase decoding of elliptic codes through computing the Gröbner basis – year: 2001 ident: ref29 article-title: List decoding of linear block codes – ident: ref5 doi: 10.1109/18.817522 – ident: ref18 doi: 10.1109/TIT.2010.2046208 – ident: ref33 doi: 10.1109/TIT.2020.3042248 – ident: ref27 doi: 10.1109/TCOMM.2020.3011991 – ident: ref19 doi: 10.1109/TIT.2009.2039073 |
| SSID | ssj0004033 |
| Score | 2.485377 |
| Snippet | This paper proposes the low-complexity Chase (LCC) decoding for Hermitian codes, which is facilitated by both the improved interpolation and root-finding. By... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 5509 |
| SubjectTerms | Algorithms Basis reduction Codes Complexity Complexity theory Decoding early termination Encoding fast root-finding Galois fields Hermitian codes Interpolation Maximum likelihood decoding Polynomials re-encoding transform Reliability Symbols Transforms |
| Title | Low-Complexity Chase Decoding of Hermitian Codes With Improved Interpolation and Root-Finding |
| URI | https://ieeexplore.ieee.org/document/10818514 https://www.proquest.com/docview/3246560155 |
| Volume | 73 |
| WOSCitedRecordID | wos001551629100022&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1558-0857 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004033 issn: 0090-6778 databaseCode: RIE dateStart: 19720101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NS8NAEF20eNCDnxWrVfbgTbZus0k2e5Ro6cFWkYq9SEizs7SXRNpU8d87u0mxIh6EHALZQJjJZN5s3psh5FJEEfgqBKa5lzHf-ClD1BqyAKGu6oKQ3HA3bEIOh9F4rB5rsbrTwgCAI59Bx566f_m6yJZ2qwwj3KYXO7Z6U0pZibW-RZBc1C0nLZ9dRiuFDFfXo_hhMMBa0PM7iDdwYfAjC7mxKr--xS7B9Pb--Wj7ZLdGkvSmcv0B2YD8kOys9Rc8Iq_3xQezEW-7XpafNJ5izqK3WHHajEULQ_uWC2ODnMaFhgV9mZVTWm00gKYVI7Go6HI0zTV9KoqS9WZOCtMkz727Udxn9TwFlnm-LJmAsDuRGqNQc-OJDIS2HDV0kOIQcA0cYKI8GRmepSbAIzATIVJEFOABmu2YNPIihxNCM2WE9o3GAlf5OkyVykIeGQxn6Ud4sUWuVvZN3qq2GYkrN7hKnDcS642k9kaLNK1F11ZWxmyR9sonSR1aiwQRoG0YhDjo9I_bzsi2Z6f0OppemzTK-RLOyVb2Xs4W8wv31nwBuI6_Cg |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NS8NAEF1EBfXgZ8Vq1T14k63b7OZjj1ItFdsqUrEXCWl2lvbSSJsq_ntnNylWxIOQQyAbCDOZzJvNezOEXIgoAqkCYJp7KZNGJgxRa8B8hLqqASLkhrthE2GvFw0G6rEUqzstDAA48hnU7an7l6-zdG63yjDCbXqxY6vXfCm9RiHX-pZBclE2nbSM9jBaaGS4uuo3H7pdrAY9WUfEgQv9H3nIDVb59TV2Kaa188-H2yXbJZak14Xz98gKTPbJ1lKHwQPy2sk-mI152_cy_6TNEWYteoM1p81ZNDO0bdkwNsxpM9Mwoy_jfESLrQbQtOAkZgVhjiYTTZ-yLGetsRPDVMhz67bfbLNyogJLPRnmTEDQGIYa41Bz44kUhLYsNXSR4uBzDRxgqLwwMjxNjI-Hb4ZCJIgpwAM02yFZnWQTOCI0VUZoaTSWuErqIFEqDXhkMKBDGeHFKrlc2Dd-KxpnxK7g4Cp23oitN-LSG1VSsRZdWlkYs0pqC5_EZXDNYsSAtmUQIqHjP247JxvtfrcTd-569ydk07Mzex1pr0ZW8-kcTsl6-p6PZ9Mz9wZ9AdQ-wlE |
| 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-Complexity+Chase+Decoding+of+Hermitian+Codes+With+Improved+Interpolation+and+Root-Finding&rft.jtitle=IEEE+transactions+on+communications&rft.au=Liang%2C+Jiwei&rft.au=Zhao%2C+Jianguo&rft.au=Chen%2C+Li&rft.date=2025-08-01&rft.issn=0090-6778&rft.eissn=1558-0857&rft.volume=73&rft.issue=8&rft.spage=5509&rft.epage=5522&rft_id=info:doi/10.1109%2FTCOMM.2024.3524035&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TCOMM_2024_3524035 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0090-6778&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0090-6778&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0090-6778&client=summon |