A coded modulation scheme for deep-space optical communications is proposed, which is composed of an outer singleparity- check (SPC)-based product code, an interleaver, a bit-accumulator and a pulse-position modulation (PPM). It is referred as SPC-APPM code, which is decoded with an iterative demodulator-decoder using standard turbo-decoding techniques. Investigations show that the scheme has the advantages of low encoding and decoding complexities, good performance and flexible code rate for all rates above 1/2. Meanwhile, simulation results demonstrate that the SPC-APPM provides the performance similar to the low-density parity-check-APPM (LDPC-APPM), superior to the LDPC-PPM and product accumulate code-PPM (PA-PPM), although inferior to serially concatenated PPM (SCPPM). At the bit error rate (BER) of 10^-5, the performance of SPC-APPM is about 0.7 dB better than LDPC-PPM and 1.2 dB better than PA-PPM.