Protocol Sequences for Multiple-Packet Reception
  Consider a time slotted communication channel shared by $K$ active users and a single receiver. It is assumed that the receiver has the ability of the multiple-packet reception (MPR) to correctly receive at most $\gamma$ ($1 \leq \gamma < K$) simultaneously transmitted packets. Each user accesses the channel following a specific periodical binary sequence, called the protocol sequence, and transmits a packet within a channel slot if and only if the sequence value is equal to one. The fluctuation in throughput is incurred by inevitable random relative shifts among the users due to the lack of feedback. A set of protocol sequences is said to be throughput-invariant (TI) if it can be employed to produce invariant throughput for any relative shifts, i.e., maximize the worst-case throughput. It was shown in the literature that the TI property without considering MPR (i.e., $\gamma=1$) can be achieved by using shift-invariant (SI) sequences, whose generalized Hamming cross-correlation is independent of relative shifts. This paper investigates TI sequences for MPR; results obtained include achievable throughput value, a lower bound on the sequence period, an optimal construction of TI sequences that achieves the lower bound on the sequence period, and intrinsic structure of TI sequences. In addition, we present a practical packet decoding mechanism for TI sequences that incorporates packet header, forward error-correcting code, and advanced physical layer blind signal separation techniques. 
Yijin Zhang, Yuan-Hsun Lo, Feng Shu and Wing Shing Wong
cs.IT math.IT