In this paper, a family of linear congruence sequences with interesting cross-correlation properties is investigated for potential applications in defining new multiple access protocols for distributed wireless systems. One can show that for any finite subset of the sequences with rate sum not exceeding a certain level, there cannot have enough collisions to completely block any particular user no matter how they are shifted with respect to one another. The user un-suppressibility and service guarantee can be exploited in many applications such as wireless sensor or impulse radio systems. To enhance the system's allowable rate sum while possessing the non-blocking property, new protocol sequences are designed. Besides, the throughput shift-invariant property is obtained.