Iterative Soft-Decision Decoding of Hermitian Codes

This paper proposes an iterative soft-decision decoding algorithm for one of the most popular algebraic-geometric (AG) codes - Hermitian codes. The algorithm is designed by integrating the two most powerful soft-decision decoding algorithms, the adaptive belief propagation (ABP) algorithm and the Ko...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 61; no. 1; pp. 33 - 42
Main Author: Chen, Li
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2013
Institute of Electrical and Electronics Engineers
Subjects:
Adaptive belief propagation
algebraic-geometric codes
Algorithm design and analysis
Applied sciences
Coding, codes
complexity reduction
Complexity theory
Decoding
Exact sciences and technology
Hermitian codes
Information, signal and communications theory
Iterative decoding
Koetter-Vardy algorithm
list decoding
Polynomials
Reed-Solomon Codes
Reliability
Signal and communications theory
Telecommunications and information theory
Vectors
Reed Solomon code
Performance evaluation
Hermitian codes, iterative decoding
Hermite interpolation
Adaptive belief propagation
Algorithm
Iterative decoding
Geometrical model
Credal approach
list decoding
Algebraic geometric codes
complexity reduction
Soft decision
Reliability
Koetter-Vardy algorithm
Reed-Solomon Codes
Parity check
algebraic-geometric codes
ISSN:0090-6778
Online Access:Get full text
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Summary:This paper proposes an iterative soft-decision decoding algorithm for one of the most popular algebraic-geometric (AG) codes - Hermitian codes. The algorithm is designed by integrating the two most powerful soft-decision decoding algorithms, the adaptive belief propagation (ABP) algorithm and the Koetter-Vardy (KV) list decoding algorithm. The ABP algorithm performs iterative decoding based on an adapted parity-check matrix of a Hermitian code to enhance the reliability of the soft received information. With the enhanced reliability, the KV algorithm performs soft-decision list decoding to obtain the original message. Since the matrix adaptation relies on bit reliabilities, regrouping of the unreliable bits is introduced to assist the ABP decoding. A complexity reducing ABP-KV decoding approach is proposed based on assessing the soft information provided by the ABP algorithm and determining whether the following KV decoding steps should be carried out. Geometric interpretation of the ABP algorithm is presented, demonstrating the necessity of performing matrix adaptation. Our performance analysis shows the proposed iterative decoding algorithm outperforms both the existing decoding approaches for Hermitian codes and the ABP-KV decoding of Reed-Solomon (RS) codes.
ISSN:0090-6778
DOI:10.1109/TCOMM.2012.100512.110871