Protocol Sequences for Multiple-Packet Reception

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. Shift-invariant (SI) sequences form an important class of protocol sequences which enjoy perfect crosscorrelation property. It was proved that they can produce zero-variance throughput for γ = 1. In this paper we investigate a broader class of protocol sequences which have zero-variance throughput considering MPR, but may have non-perfect crosscorrelation property. Such protocol sequences are said to be throughput-invariant (TI). First, we derive the value of constant individual throughput of TI sequences for any γ. Second, lower bounds on the sequence period for any γ are presented. Third, we prove that SI sequences are indeed TI for any γ, and the shortest SI sequences are optimal for any γ < K in the sense that the sequence period achieves the lower bound. Lastly, it is shown that SI property is intrinsic for TI sequences in some cases. Index Terms Collision channel without feedback, protocol sequences, multiple-packet reception.