MIMO-constant envelop modulation (CEM) is a very power and complexity efficient system, which is introduced as alternative candidate to the currently used MIMO-Orthogonal Frequency Division Multiplexing (OFDM). CEM system enables to use high efficient nonlinear power amplifier on the transmitter side and 1 bit (low resolution) analog to digital converter (ADC) on the receiver side. Due to adopting the low resolution at the receiver side a great reduction in hardware complexity and power consumption can be achieved. However, there will be a noticeable degradation on the performance of bit error rate (BER) on the receiver side due to sever quantization error introduced by the low-resolution ADC, so a forward error correction coding is essential to enhance the BER. In this paper a LDPC coded MIMO-CEM system was used as a replacement for MIMO-OFDM to deal with the BER degradation problem of the CEM system. The performance of the LDPC coded MIMO-CEM with Gaussian Minimum Phase Shift Keying (GMSK) modulation is evaluated over a multi-path Rayleigh fading channel. It showed that LDPC codes are effective to improve the BER performance of CEM on Rayleigh fading channels. According to the simulation results, the MIMO-CEM system provides a significant improvement in BER performance and outperforms the un-coded and the original convolutional coder based CEM systems.