In this paper, a class of periodic unipolar binary sequences are investigated for their potential applications in defining new protocols for distributed wireless multiple access. Based on linear congruence sequences, one can show that for any finite subset of these sequences with total proportional rate not exceeding a specific threshold, there cannot be enough collisions to completely block any particular sequence, no matter how they are shifted with respect to one another. This property can be exploited in certain applications such as wireless sensor and ad hoc networks. A further investigation on how to enhance the allowable rate sum is carried out. New protocol sequences with interesting and useful properties are designed accordingly.