Design and Analysis of Nonbinary LDPC Codes for Arbitrary Discrete-Memoryless Channels

We present an analysis, under iterative decoding, of coset 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 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 AWGN channel, including results within 0.56 dB of the unconstrained Shannon limit (i.e. not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.Comment: To appear, IEEE Transactions on Information Theory, (submitted October 2004, revised and accepted for publication, November 2005). The material in this paper was presented in part at the 41st Allerton Conference on Communications, Control and Computing, October 2003 and at the 2005 IEEE International Symposium on Information Theor

Simplification Resilient LDPC-Coded Sparse-QIM Watermarking for 3D-Meshes

We propose a blind watermarking scheme for 3-D meshes which combines sparse quantization index modulation (QIM) with deletion correction codes. The QIM operates on the vertices in rough concave regions of the surface thus ensuring impeccability, while the deletion correction code recovers the data hidden in the vertices which is removed by mesh optimization and/or simplification. The proposed scheme offers two orders of magnitude better performance in terms of recovered watermark bit error rate compared to the existing schemes of similar payloads and fidelity constraints.Comment: Submitted, revised and Copyright transfered to IEEE Transactions on Multimedia, October 9th 201