On the characterization of statistically synchronizable variable-length codes

The authors consider statistically synchronizable variable-length codes, i.e. codes that admit decoders able to self-synchronize with high probability if the input sequence of code symbols is long enough. They show that a necessary and sufficient condition for the existence of a statistically self-synchronizing decoder and, therefore, for a code to be statistically synchronizable, is that the code has a synchronizing sequence. They also give a decision procedure to test whether a code has a synchronizing sequence. Finally, they specialize the procedure to obtain a simple and efficient algorithm to test the statistical synchronizability property of prefix codes.>