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...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on communications Vol. 66; no. 4; pp. 1376 - 1385
Main Authors: Siyuan Wu, Li Chen, Johnston, Martin
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2017.2786667