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This work proposes a tractable estimation of the maximum a posteriori (MAP)threshold of various families of sparse-graph code ensembles, by using anapproximation for the extended belief propagation generalized extrinsicinformation transfer (EBP-GEXIT) function, first proposed by Measson et al. Weconsider the transmission over non-binary complex-input additive white Gaussiannoise channel and extend the existing results to obtain an expression for theGEXIT function. We estimate the MAP threshold by applying the Maxwellconstruction to the obtained approximate EBP-GEXIT charts for various familiesof low-density parity-check (LDPC), generalized LDPC, doubly generalized LDPC,and serially concatenated turbo codes (SC-TC). When codewords of SC-TC aremodulated using Gray mapping, we also explore where the spatially-coupledbelief propagation (BP) threshold is located with respect to the previouslycomputed MAP threshold. Numerical results indicate that the BP threshold of thespatially-coupled SC-TC does saturate to the MAP threshold obtained viaEBP-GEXIT chart.

EBP-GEXIT Charts for M-ary AWGN Channel for Generalized LDPC and Turbo Codes