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High performance non-binary quasi-cyclic LDPC codes on euclidean geometries
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Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersions
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Bounds and lattice-based transmission strategies for the phase-faded dirty-paper channel
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Linear-programming decoding of nonbinary linear codes
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Efficient LDPC codes over GF(q) for Lossy data compression
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Iterative approximate linear programming decoding of LDPC codes with linear complexity
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A class of quasi-cyclic LDPC codes over GF(2m)
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Performance bounds for nonbinary linear block codes over memoryless symmetric channels
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Density evolution for nonbinary LDPC codes under Gaussian approximation
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Near-Shannon-limit linear-time-encodable nonbinary irregular LDPC codes
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ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Low-complexity decoding for non-binary LDPC codes in high order fields
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Quasi-cyclic LDPC codes: an algebraic construction
IEEE Transactions on Communications
Bandwidth-efficient modulation codes based on nonbinary irregular repeat-accumulate codes
IEEE Transactions on Information Theory
Efficient decoder design for nonbinary quasicyclic LDPC codes
IEEE Transactions on Circuits and Systems Part I: Regular Papers - Special issue on ISCAS 2009
A subp-optimal log-domain decoding algorithm for non-binary LDPC codes
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Group codes outperform binary-coset codes on nonbinary symmetric memoryless channels
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Design of nonbinary LDPC codes over GF(q) for multiple-antenna transmission
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Decoding and Design of LDPC Codes for High-Order Modulations
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Two low-complexity reliability-based message-passing algorithms for decoding non-binary LDPC codes
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Wireless Personal Communications: An International Journal
Unified and optimized linear collision attacks and their application in a non-profiled setting
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
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We present an analysis under the iterative decoding of coset low-density parity-check (LDPC) codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random- coset analysis to produce an effect that is similar to output symmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q-1-dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop extrinsic information transfer (EXIT) charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the additive white Gaussian noise (AWGN) channel, including results within 0.56 dB of the unrestricted Shannon limit (i.e., not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.