Detection/decoding over channels with synchronization errors and inter-symbol interference

We consider coding schemes over an independent and identically distributed (i.i.d.) insertion/deletion channel with inter-symbol interference (ISI). The idea is based on a serial concatenation of a low-density parity check (LDPC) code with a marker code. First, we design a maximum-a-posteriori (MAP) detector operating at the bit level which jointly achieves synchronization for the insertion/deletion channel (with the help of the marker code) and equalization for the ISI channel. Utilizing this MAP detector together with an LDPC code with powerful error-correction capabilities, we demonstrate that reliable transmission over this channel is feasible. Then, we consider low-complexity channel detection algorithms needed for proper synchronization/equalization. Specifically, we use separate synchronization and equalization algorithms instead of joint detection and also explore the performance of M- and T-algorithms implemented as low complexity soft output channel detectors. Such schemes greatly reduce the amount of computations needed at the cost of some performance loss as illustrated via a set of simulation results.