  This work proposes a tractable estimation of the maximum a posteriori (MAP)
threshold of various families of sparse-graph code ensembles, by using an
approximation for the extended belief propagation generalized extrinsic
information transfer (EBP-GEXIT) function, first proposed by Measson et al. We
consider the transmission over non-binary complex-input additive white Gaussian
noise channel and extend the existing results to obtain an expression for the
GEXIT function. We estimate the MAP threshold by applying the Maxwell
construction to the obtained approximate EBP-GEXIT charts for various families
of low-density parity-check (LDPC), generalized LDPC, doubly generalized LDPC,
and serially concatenated turbo codes (SC-TC). When codewords of SC-TC are
modulated using Gray mapping, we also explore where the spatially-coupled
belief propagation (BP) threshold is located with respect to the previously
computed MAP threshold. Numerical results indicate that the BP threshold of the
spatially-coupled SC-TC does saturate to the MAP threshold obtained via
EBP-GEXIT chart.
