Time-varying block codes for synchronisation errors : maximum a posteriori decoder and practical issues

Abstract

In this study, the authors consider time-varying block (TVB) codes, which generalise a number of previous synchronisation error correcting codes. They also consider various practical issues related to maximum a posteriori (MAP) decoding of these codes. Specifically, they give an expression for the expected distribution of drift between transmitter and receiver because of synchronisation errors. They determine an appropriate choice for state space limits based on the drift probability distribution. In turn, they obtain an expression for the decoder complexity under given channel conditions in terms of the state space limits used. For a given state space, they also give a number of optimisations that reduce the algorithm complexity with no further loss of decoder performance. They 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, they 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.