In this paper, we consider coded multi-input multi-output (MIMO) systems with low-density parity-check (LDPC) codes and space-time block code (STBC) in MIMO channels. The LDPC code takes the role of a channel code while the STBC provides spatial-temporal diversity. The performance of such coded MIMO system has been shown to be excellent in the past. In this paper, we present a performance analysis for an upper bound on probability of error for coded MIMO schemes. Compared to previous works, the proposed approach for the upper bound can avoid any explicit weight enumeration of codewords and provide a significant step for the upper bound by using a multinomial theorem. In addition, we propose a log domain convolution that enables us to handle huge numbers, e.g., 10500. Comparison of system simulations and numerical evaluations shows that the proposed upper bound is applicable for various coded MIMO systems.