Introduction to finite fields and their applications
Introduction to finite fields and their applications
IEEE Transactions on Communications
High performance non-binary quasi-cyclic LDPC codes on euclidean geometries
IEEE Transactions on Communications
Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersions
IEEE Transactions on Communications
Good error-correcting codes based on very sparse matrices
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
Weighted nonbinary repeat-accumulate codes
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
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
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This paper presents two new large classes of QCLDPC codes, one binary and one non-binary. Codes in these two classes are constructed by array dispersions of row-distance constrained matrices formed based on additive subgroups of finite fields. Experimental results show that codes constructed perform very well over the AWGN channel with iterative decoding based on belief propagation. Codes of a subclass of the class of binary codes have large minimum distances comparable to finite geometry LDPC codes and they offer effective tradeoff between error performance and decoding complexity when decoded with low-complexity reliability-based iterative decoding algorithms such as binary message passing decoding algorithms. Non-binary codes decoded with a Fast-Fourier Transform based sum-product algorithm achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either the hard-decision Berlekamp-Massey algorithm or the algebraic soft-decision Kötter-Vardy algorithm. They have potential to replace Reed-Solomon codes in some communication or storage systems where combinations of random and bursts of errors (or erasures) occur.