We formulate an optimization problem for designing nonuniformly spaced constellations for equiprobable M-ary coded modulation schemes. Given the average channel SNR constraint, optimum (equiprobable) signal sets are obtained in an attempt to maximize the mutual information between channel input and output. It is proved that the optimum signal set can asymptotically achieve the ultimate Shannon capacity over an AWGN channel without requiring any shaping technique. Extensive comparisons between the optimum signal set, a geometrically Gaussian-like signal set, and a uniformly spaced signal set are provided. Extensions to Rayleigh fading channels are also investigated. Rather than using a trellis code to exploit the performance gain of the optimum signal constellation, we investigate powerful low-density parity-check codes over GF(2*b) in conjunction with 2(*b)-ary) modulation schemes. Simulation results show that such a coding scheme can exploit almost the entire performance gain promised by the information-theoretic argument.
By: Xiao--Yu Hu
Published in: RZ3385 in 2001
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