In this paper, coded multiple-input-multiple-output (MIMO) communication schemes for data transmission over the optical atmospheric turbulence channels are studied. Two strategies are proposed and compared. The first is based on repetition coding, and the second on space-time (ST) coding. Both approaches employ low-density parity-check (LDPC) codes. The LDPC codes are designed using the concept of pairwise balanced design (PBD), balanced incomplete block design (BIBBD), and block-circulant (array) codes. To improve the spectral efficiency, we employ a bit-interleaved (BI) LDPC-coded modulation based on the pulse amplitude modulation (PAM). A better bit error rate (BER) performance is achieved by the iteration of extrinsic information between a demapper and LDPC decoder. The simulations show that the LDPC-coded MIMO schemes can operate under a strong atmospheric turbulence and at the same time provide excellent coding gains compared with the transmission of uncoded data. To verify the efficiency of the proposed coding schemes, achievable information rates are computed when the turbulence is modeled by a gamma-gamma distribution.