Counterexamples: The prefix code {00, 11} is not self-synchronizing; while 0, 1, 01 and 10 are not codes, 00 and 11 are. The prefix code {ab,ba} is not self-synchronizing because abab contains ba. The prefix code b∗a (using the Kleene star) is not self-synchronizing (even though any new code word simply starts after a) because code word ba contains code word a.
Counterexamples: The prefix code {00, 11} is not self-synchronizing; while 0, 1, 01 and 10 are not codes 00 and 11 are. The prefix code {ab,ba} is not self-synchronizing because abab contains ba. The prefix code b∗a (using the Kleene star) is not self-synchronizing (even though any new code word simply starts after a) because code word ba contains code word a.