Iterative Decoding Algorithms for a Class of Non-Binary Two-Step Majority-Logic Decodable Cyclic Codes

This paper presents two iterative decoding algorithms for a class of non-binary two-step majority-logic (NB-TS-MLG) decodable cyclic codes. A partial parallel decoding scheme is also introduced to provide a balanced trade-off between decoding speed and storage requirements. Unlike non-binary one-ste...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 62; no. 6; pp. 1779 - 1789
Main Authors: Chang, Hsiu-Chi, Chang, Hsie-Chia
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.06.2014
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Balancing
Codes
Coding, codes
Complexity theory
Decoding
Degradation
Exact sciences and technology
Gain
Geometry
Information, signal and communications theory
Iterative decoding
Matrix decomposition
Maximum likelihood decoding
Niobium
Noise levels
Signal and communications theory
Telecommunications and information theory
Tradeoffs
Vectors
cyclic codes
majority-logic decoding
Extended min-sum algorithm
non-binary LDPC codes
Reed Solomon code
Performance evaluation
Cyclic code
Majority logic
Tanner graph
Algorithm
Binary code
Iterative decoding
Simulation
Coding
Error correcting code
Parity check codes
Soft decision
Parity check
ISSN:0090-6778, 1558-0857
Online Access:Get full text
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Summary:This paper presents two iterative decoding algorithms for a class of non-binary two-step majority-logic (NB-TS-MLG) decodable cyclic codes. A partial parallel decoding scheme is also introduced to provide a balanced trade-off between decoding speed and storage requirements. Unlike non-binary one-step MLG decodable cyclic codes, the Tanner graphs of which are 4-cycle-free, NB-TS-MLG decodable cyclic codes contain a large number of short cycles of length 4, which tend to degrade decoding performance. The proposed algorithms utilize the orthogonal structure of the parity-check matrices of the codes to resolve the degrading effects of the short cycles of length 4. Simulation results demonstrate that the NB-TS-MLG decodable cyclic codes decoded with the proposed algorithms offer coding gains as much as 2.5 dB over Reed-Solomon codes of the same lengths and rates decoded with either hard-decision or algebraic soft decision decoding.
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2014.2320508