Interpolation-Based Low-Complexity Chase Decoding Algorithms for Hermitian Codes

Algebraic-geometric (AG) codes have good error-correction capability due to their generally large code word length. However, their decoding remains complex, preventing practical applications. Addressing the challenge, this paper proposes two interpolation-based low-complexity Chase (LCC) decoding al...

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Vydané v:IEEE transactions on communications Ročník 66; číslo 4; s. 1376 - 1385
Hlavní autori: Siyuan Wu, Li Chen, Johnston, Martin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.04.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Adaptive algorithms
adaptive decoding
Algebra
Algebraic-geometric codes
Algorithm design and analysis
Algorithms
Chase decoding
Codes
Complexity
Complexity theory
Computer simulation
Decoding
Error correction
Hamming distance
Hermitian codes
Interpolation
Mathematical analysis
Reliability
Reliability aspects
Simulation
Vectors (mathematics)
ISSN:0090-6778, 1558-0857
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Abstract Algebraic-geometric (AG) codes have good error-correction capability due to their generally large code word length. However, their decoding remains complex, preventing practical applications. Addressing the challenge, this paper proposes two interpolation-based low-complexity Chase (LCC) decoding algorithms for one of the most popular AG codes-Hermitian codes. By choosing η unreliable symbols and realizing them with the two most likely decisions, 2 η decoding test-vectors can be formulated. The first LCC algorithm performs interpolation for the common elements of the test-vectors, producing an intermediate outcome that will be shared by the uncommon element interpolation. It eliminates the redundant computation for decoding each test-vector, resulting in a low-complexity. With an interpolation multiplicity of one, the decoding is further facilitated by removing the requirement of pre-calculating the Hermitian curve's corresponding coefficients. The second LCC algorithm is an adaptive variant of the first algorithm, where the number of test-vectors is determined by the reliability of received information. When the channel condition improves, it can reduce the complexity without compromising the decoding performance. Simulation results show that the both LCC algorithms outperform a number of existing algebraic decoding algorithms for Hermitian codes. Finally, our complexity analysis will reveal the proposals' low-complexity feature.
AbstractList Algebraic-geometric (AG) codes have good error-correction capability due to their generally large code word length. However, their decoding remains complex, preventing practical applications. Addressing the challenge, this paper proposes two interpolation-based low-complexity Chase (LCC) decoding algorithms for one of the most popular AG codes-Hermitian codes. By choosing η unreliable symbols and realizing them with the two most likely decisions, 2 η decoding test-vectors can be formulated. The first LCC algorithm performs interpolation for the common elements of the test-vectors, producing an intermediate outcome that will be shared by the uncommon element interpolation. It eliminates the redundant computation for decoding each test-vector, resulting in a low-complexity. With an interpolation multiplicity of one, the decoding is further facilitated by removing the requirement of pre-calculating the Hermitian curve's corresponding coefficients. The second LCC algorithm is an adaptive variant of the first algorithm, where the number of test-vectors is determined by the reliability of received information. When the channel condition improves, it can reduce the complexity without compromising the decoding performance. Simulation results show that the both LCC algorithms outperform a number of existing algebraic decoding algorithms for Hermitian codes. Finally, our complexity analysis will reveal the proposals' low-complexity feature.
Algebraic-geometric (AG) codes have good error-correction capability due to their generally large code word length. However, their decoding remains complex, preventing practical applications. Addressing the challenge, this paper proposes two interpolation-based low-complexity Chase (LCC) decoding algorithms for one of the most popular AG codes-Hermitian codes. By choosing η unreliable symbols and realizing them with the two most likely decisions, 2η decoding test-vectors can be formulated. The first LCC algorithm performs interpolation for the common elements of the test-vectors, producing an intermediate outcome that will be shared by the uncommon element interpolation. It eliminates the redundant computation for decoding each test-vector, resulting in a low-complexity. With an interpolation multiplicity of one, the decoding is further facilitated by removing the requirement of pre-calculating the Hermitian curve's corresponding coefficients. The second LCC algorithm is an adaptive variant of the first algorithm, where the number of test-vectors is determined by the reliability of received information. When the channel condition improves, it can reduce the complexity without compromising the decoding performance. Simulation results show that the both LCC algorithms outperform a number of existing algebraic decoding algorithms for Hermitian codes. Finally, our complexity analysis will reveal the proposals' low-complexity feature.
Author Johnston, Martin
Li Chen
Siyuan Wu
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Cites_doi 10.1109/ICC.2007.145
10.1109/TIT.1969.1054260
10.1007/3-540-46796-3_26
10.1109/18.782097
10.1109/TIT.2003.819332
10.1109/TIT.2009.2039073
10.1109/18.720550
10.1109/T-WC.2008.070615
10.1109/18.476240
10.1109/TCOMM.2009.08.070302
10.1109/18.945273
10.1109/18.179340
10.1109/TIT.2010.2046208
10.1049/ip-com:20045153
10.1006/jcom.1997.0439
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References ref13
nielsen (ref14) 2001
ref11
ref10
ref2
ref17
ref16
ref19
ref18
ref8
chen (ref12) 2008
ref7
ref9
ref4
ref3
ref6
ref5
goppa (ref1) 1981; 24
köetter (ref15) 1996
References_xml – ident: ref17
  doi: 10.1109/ICC.2007.145
– ident: ref2
  doi: 10.1109/TIT.1969.1054260
– ident: ref18
  doi: 10.1007/3-540-46796-3_26
– ident: ref7
  doi: 10.1109/18.782097
– ident: ref8
  doi: 10.1109/TIT.2003.819332
– volume: 24
  start-page: 170
  year: 1981
  ident: ref1
  article-title: Codes on algebraic curves
  publication-title: Soviet Math Dokl
– ident: ref11
  doi: 10.1109/TIT.2009.2039073
– ident: ref13
  doi: 10.1109/18.720550
– ident: ref19
  doi: 10.1109/T-WC.2008.070615
– year: 1996
  ident: ref15
  article-title: On algebraic decoding of algebraic-geometric and cyclic codes
– ident: ref3
  doi: 10.1109/18.476240
– ident: ref9
  doi: 10.1109/TCOMM.2009.08.070302
– ident: ref16
  doi: 10.1109/18.945273
– ident: ref4
  doi: 10.1109/18.179340
– ident: ref10
  doi: 10.1109/TIT.2010.2046208
– ident: ref5
  doi: 10.1049/ip-com:20045153
– ident: ref6
  doi: 10.1006/jcom.1997.0439
– year: 2001
  ident: ref14
  article-title: List decoding of linear block codes
– year: 2008
  ident: ref12
  article-title: Design of an efficient list decoding system for Reed-Soloman and alebraic geometric codes
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SubjectTerms Adaptive algorithms
adaptive decoding
Algebra
Algebraic-geometric codes
Algorithm design and analysis
Algorithms
Chase decoding
Codes
Complexity
Complexity theory
Computer simulation
Decoding
Error correction
Hamming distance
Hermitian codes
Interpolation
Mathematical analysis
Reliability
Reliability aspects
Simulation
Vectors (mathematics)
Title Interpolation-Based Low-Complexity Chase Decoding Algorithms for Hermitian Codes
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