Synchronizable codes for the optical OPPM channel

Random overlapping pulse-position modulation (OPPM) sequences result in an unrecoverable error floor on both the probability of erroneous synchronization and the probability of symbol error when only chip synchronization is present. It is known, however, that for a given sequence length M, a subset of the set of all possible sequences is synchronizable in the sense that in the absence of noise, the receiver can correctly symbol synchronize by observing M or more symbol intervals. The authors design finite-state machines and codes over a J-ary alphabet, which produce sequences with the property that every subsequence of length L is synchronizable. Some of the codes, in addition to being synchronizable, produce a coding gain. For an optical Poisson channel the authors introduce joint synchronization and detection algorithms that utilize the memory in the encoded sequences to produce joint estimates of timing and sequences. Their performance is analyzed through simulations and analytical results