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A coded modulation scheme for deep-space optical communications is studied, which is a serial concatenation of an outer low-density parity-check (LDPC) code, an interleaver, a bit-accumulator, and pulse-position modulation (PPM). It is referred as LDPC-APPM. It is decoded with an iterative demodulator-decoder using standard turbo-decoding techniques. Simulation results show that the LDPC-APPM with an outer LDPC code of medium code length suffers a loss of about 0.7 dB at a bit-error rate of relative to the serially concatenated PPM (SCPPM) of similar parameters, which consists of the serial concatenation of an outer convolutional code, an interleaver, a bit-accumulator, and PPM; however, it has better code rate flexibility especially for high rates and simpler implementation structure than SCPPM. Further, it can achieve better performance than the LDPC-PPM of the same rate and length, which consists of the serial concatenation of an LDPC code and PPM.