In free-space optical(FSO) communications, the performance of the communication systems is severely degraded by atmospheric turbulence. Channel coding and diversity techniques are commonly used to combat channel fading induced by atmospheric turbulence. In this paper, we present the generalized block Markov superposition transmission(GBMST) of repetition codes to improve time diversity. In the GBMST scheme, information sub-blocks are transmitted in the block Markov superposition manner, with possibly different transmission memories. Based on analyzing an equivalent system, a lower bound on the bit-error-rate(BER) of the proposed scheme is presented. Simulation results demonstrate that, under a wide range of turbulence conditions, the proposed scheme improves diversity gain with only a slight reduction of transmission rate. In particular, with encoding memory sequence(0, 0, 8) and transmission rate 1/3, a diversity order of eleven is achieved under moderate turbulence conditions. Numerical results also show that, the GBMST systems with appropriate settings can approach the derived lower bound, implying that full diversity is achievable. In free-space optical (FSO) communications, the performance of the communication systems is severely degraded by atmospheric turbulence. Channel coding and diversity techniques are commonly used to combat channel fading induced by atmospheric turbulence. In this paper, we present the generalized block Markov Based on the analysis of an equivalent system, a lower bound on the bit (GBMST) of repetition codes to improve time diversity. In the GBMST scheme, information sub-blocks are transmitted in the block Markov superposition manner, with possibly different transmission memories Simulation results demonstrate that, under a wide range of turbulence conditions, the proposed scheme improves diversity gain with only a slight reduction of transmission rate. In particular, with encoding memory sequence ( 0, 0, 8) and transmission rate 1/3, a diversity order of eleven is achieved under moderate turbulence conditions. Numeri cal results also show that, the GBMST systems with appropriate settings can approach the derived lower bound, implying that full diversity is achievable.