This paper introduces a family of periodic binary sequences with interesting cross-correlation properties for potential applications in distributed wireless accessing. Following Massey's model of collision channel without feedback, a simple and robust multiple access protocol that does not require complicated processing such as back-off algorithms or random number generation is proposed for wireless sensor and ad hoc networks. In addition, energy-efficient data reception is achievable by the protocol while continuous channel listening can be eliminated. Besides, a simple predictive collision avoidance scheme is presented for the enhancement of system throughput. Simulation studies are carried out to show its effectiveness.