Joint synchronization and decoding for photon-limited optical channels: code design and complexity reduction

In this work, we will consider the problem of joint symbol synchronization and decoding of pulse position modulation (PPM) sequences in the deep-space photon-limited optical channel, where joint synchronization and decoding is significantly superior to separate synchronization and decoding. We also consider the design of codes having both good error control and synchronization properties for use with PPM signaling on this channel. While schemes for joint synchronization and decoding on this channel have been previously investigated, the complexity of these schemes has been prohibitive. In addition, their optimality with respect to computational complexity depends on the assumption that symbols are statistically independent and hence uncoded. We propose a two-stage joint synchronizer and decoder that achieve a selected performance requirement while reducing the complexity of joint synchronizer and decoder. The complexity is reduced by terminating synchronization once this error probability requirement is achieved, at which point the synchronizer/decoder functions only as a decoder on the remaining symbols in the received sequences. Therefore, the proposed scheme has practical complexity in the deep-space photon-limited optical channel, which may be used in the future deep-space missions.