EXIT charts for non-binary LDPC codes over arbitrary discrete-memoryless channels

We consider coset LDPC codes over GF(q), designed for use over arbitrary channels (particularly nonbinary and asymmetric 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 messages produced by the decoder. We use this property to show that under a Gaussian approximation, the entire q - 1 dimensional distribution of the vector messages is described by a single scalar parameter. We apply this result 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 results for the AWGN channel at 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