Protocol sequences for multiple-packet reception: Throughput invariance and user irrepressibility

We consider the slot-synchronized collision channel without feedback, in which K active users all transmit their packets to one sink. It is assumed that the channel has the ability of the multiple-packet reception (MPR), i.e., can accommodate at most γ (1 ≤ γ < K) simultaneous transmissions. Each user accesses the channel following a specific periodical zero-one pattern, called the protocol sequence, and transmits a packet if and only if the sequence value is equal to one. The fluctuation in throughput is incurred by random relative delay offsets among the beginning of protocol sequences due to the lack of feedback. There are two different design goals in the literature: throughput invariance and user irrepressibility. The former one enjoys constant throughput independent of relative delay offsets, and the latter one guarantees a non-zero individual throughput in the worst case. However, all previous performance evaluation on these two criteria assumed that γ= 1. In this paper, we generalize these results to any γ > 1. For both design objective, we establish a lower bound on sequence period and prove the lower bound can be achieved by some construction.