On pairwise shift-invariant protocol sequences

Protocol sequences offer an approach to implement random-access channel without feedback. For these sequences, it is desirable that their cross-correlation should be as low as possible and that the length of their period should not be short. Completely shift-invariant sequences form an important class of protocol sequences which have perfect cross-correlation property but exponential growth period as a function of the number of users. We investigate in this paper a broader class of protocol sequences which are only pairwise shift-invariant. Results on minimum period and bit-pattern structure are presented.