Design of multi-edge-type LDPC codes for high-order coded modulation

A design method for bandwidth-efficient LDPC coded modulation for 2
^2m
-QAM constellations at rate (2m - 1)/(2m) in complex AWGN is presented. A multi-edge-type parameterization is used to exploit the distinct bit-channel capacities unique to high-order modulation using LDPC structures. EXIT analysis is adapted to multi-edge by introducing multi-dimensional EXIT iterated-function system analysis. Under this conceptualization, a successful decoding condition is developed by estimating fixed points of the dynamical system using its numerical gradient. Optimized ensembles are found for 16-QAM with thresholds matching the best known ensembles of equal complexity. For 64 to 1024-QAM, sufficiently high bit-channel capacities allow for extension of lower-order optimized ensembles, leading a practical nested code structure. The nested structure provides flexible rate selection with a single decoder. The gap to constrained, non-iterative capacity of all optimized code ensembles of maximum variable degree of 15 is within 0.21 dB.