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

Lookup NU author(s): Dr Li Chen, Dr Martin Johnston

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by IEEE, 2018.

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Abstract

IEEE Algebraic-geometric (AG) codes have good error-correction capability due to their generally large codeword 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 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.


Publication metadata

Author(s): Wu S, Chen L, Johnston M

Publication type: Article

Publication status: Published

Journal: IEEE Transactions on Communications

Year: 2018

Volume: 66

Issue: 4

Pages: 1376-1385

Print publication date: 01/04/2018

Online publication date: 25/12/2017

Acceptance date: 15/12/2017

Date deposited: 08/03/2018

ISSN (print): 0090-6778

ISSN (electronic): 1558-0857

Publisher: IEEE

URL: https://doi.org/10.1109/TCOMM.2017.2786667

DOI: 10.1109/TCOMM.2017.2786667


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