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Non-binary LDPC codes for orthogonal modulations: Analysis and code design

In this paper, we present a low-density parity-check coded modulation approach addressing orthogonal modulations with moderate order (between 8 and 32) over the additive white Gaussian noise channel. The proposed design is based on a constrained optimization of a non-binary low-density parity-check ensemble degree distribution, where the iterative decoding threshold is optimized via extrinsic information transfer analysis while restricting the search to degree distributions that target low error floors. For various orthogonal modulation orders, we provide useful approximations to the extrinsic information transfer functions, which enable a fast optimization with respect to the iterative decoding threshold. The approach is validated via codeword error rate Monte Carlo simulations and complemented by an error floor analysis, showing gains up to 0.8 dB at a codeword error rate of 10−4 with respect to existing designs, down to information block lengths as short as 192 bits.