Time-Varying Block Codes for Synchronization Errors: MAP Decoder and Practical Issues

In this paper we consider Time-Varying Block (TVB) codes, which generalize a number of previous synchronization error-correcting codes. We also consider various practical issues related to MAP decoding of these codes. Specifically, we give an expression for the expected distribution of drift between transmitter and receiver due to synchronization errors. We determine an appropriate choice for state space limits based on the drift probability distribution. In turn, we obtain an expression for the decoder complexity under given channel conditions in terms of the state space limits used. For a given state space, we also give a number of optimizations that reduce the algorithm complexity with no further loss of decoder performance. We also show how the MAP decoder can be used in the absence of known frame boundaries, and demonstrate that an appropriate choice of decoder parameters allows the decoder to approach the performance when frame boundaries are known, at the expense of some increase in complexity. Finally, we express some existing constructions as TVB codes, comparing performance with published results, and showing that improved performance is possible by taking advantage of the flexibility of TVB codes.