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In this work, a non-binary low density parity check (LDPC) coded high dimensional multiple input multiple output (MIMO) scheme with partial mapping for high order modulation is proposed. For the proposed scheme, when <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-ary quadrature amplitude modulation (QAM) is employed, then non-binary LDPC code constructed over Galois field with order <inline-formula> <tex-math notation="LaTeX">$\sqrt {M}$ </tex-math></inline-formula> is used for partial mapping, where <inline-formula> <tex-math notation="LaTeX">$\sqrt {M}$ </tex-math></inline-formula> is an integer. At the receiver side, a real-valued expectation propagation (REP) based detection algorithm is used to couple with the non-binary decoder seamlessly. Meanwhile, the symbol-wise <italic>a-priori</italic> information returned by the non-binary decoder is used to aid the REP detection. Furthermore, a symbol-wise extrinsic information transfer (SEXIT) chart based iterative optimization algorithm is used to optimize the concatenated non-binary LDPC code. This work proposed to model the <italic>a-priori</italic> information of non-zero codes/symbols of detector/decoder as the output of a cyclic-symmetric additive white Gaussian noise (AWGN) channel and a simplified method based on interpolation is proposed to calculate the component-EXIT chart of the REP-detector for massive MIMO. The proposed method can facilitate the optimization and avoid a large amount of simulations. Both SEXIT chart based analysis and numerical simulation results demonstrate the validity of the above idea.