Design and construction of protocol sequences: Shift invariance and user irrepressibility

Protocol sequences are used for channel access in the collision channel without feedback. Each user is assigned a deterministic zero-one pattern, called protocol sequence. The zeros and ones in a protocol sequence are read out periodically, and a packet is sent if and only if it is one. A collision occurs if two or more users transmit at the same time. Due to the lack of feedback from the receiver and cooperation among users, the beginning of the protocol sequences cannot be synchronized and relative delay offsets are incurred. We study the design of protocol sequences from two different perspectives. Under the first one, called shift invariance, we aim at minimizing the fluctuation of throughput due to relative delay offsets. As for the second one, called user irrepressibility, we want to guarantee that each user can send at least one packet successfully in each period. For both design criteria, we derive a lower bound on sequence period and give an optimal construction that achieves this lower bound.