This paper presents and compares two iterative coded modulation techniques for deep-space optical communications using pulse-position modulation (PPM). The first code, denoted by SCPPM, consists of the serial concatenation of an outer convolutional code, an interleaver, a bit accumulator, and PPM. The second code, denoted by LDPC-PPM, consists of the serial concatenation of an LDPC code and PPM. We employ Extrinsic Information Transfer (EXIT) charts for their analysis and design. Under conditions typical of a communications link from Mars to Earth, SCPPM is 1 dB away from capacity, while LDPC-PPM is 1.4 dB away from capacity, at a Bit Error Rate (BER) of approximately 10-5. However, LDPC-PPM lends itself naturally to low latency parallel processing in contrast to SCPPM.

Traditional constellations are uniformally spaced. By giving up uniform spacing, constellations can be designed to have larger joint (i.e. overall) capacity or parallel decoding capacity. In this paper non-uniformally spaced (i.e. 'geometrically' shaped) constellations are designed to maximize either of these quantities. By way of numerical capacity computations we show that except in special cases, there are no universally optimal geometrically shaped constellations across all code rates, and that the optimization of a constellation has to target a specific code rate. Unlike joint capacity, optimizing for parallel decoding capacity is label dependent. For PAM and PSK constellations, we found the maximum parallel decoding capacity to be achieved using gray (not necessarily binary reflective gray) labels. However, for PAM constellations, not all gray labels can yield the highest parallel decoding capacity. Besides the conventional use of a (log2(M) -1) /log2(M) code rate with an M-point constellation for bandwidth efficient communications, the optimized constellations could offer further non-trivial gains at lower code rates (unlike traditional constellations). An optimized constellation is used with a state-of-the-art LDPC code and simulation results are presented. This paper also draws a distinction between probabilistic shaping and geometric shaping and in fact proves under broad conditions, that any gain in capacity which can be found via probabilistic shaping can also be achieved or exceeded solely through geometric shaping.