Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
The Mathematical Theory of Coding
The Mathematical Theory of Coding
Error Control Coding, Second Edition
Error Control Coding, Second Edition
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Algebraic soft-decision decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels
IEEE Transactions on Information Theory
Construction of Regular and Irregular LDPC Codes: Geometry Decomposition and Masking
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Iterative algebraic soft-decision list decoding of Reed-Solomon codes
IEEE Journal on Selected Areas in Communications
Quasi-cyclic LDPC codes: an algebraic construction
IEEE Transactions on Communications
Quasi-cyclic LDPC codes: an algebraic construction, rank analysis, and codes on Latin squares
IEEE Transactions on Communications
Two low-complexity reliability-based message-passing algorithms for decoding non-binary LDPC codes
IEEE Transactions on Communications
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This paper presents algebraic methods for constructing high performance and efficiently encodable non-binary quasi-cyclic LDPC codes based on flats of finite Euclidean geometries and array masking. Codes constructed based on these methods perform very well over the AWGN channel. With iterative decoding using a Fast Fourier Transform based sum-product algorithm, they achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision Kötter-Vardy algorithm. Due to their quasi-cyclic structure, these non-binary LDPC codes on Euclidean geometries can be encoded using simple shift-registers with linear complexity. Structured non-binary LDPC codes have a great potential to replace Reed-Solomon codes for some applications in either communication or storage systems for combating mixed types of noise and interferences.