CRT Sequences With Applications to Collision Channels Allowing Successive Interference Cancellation

Protocol sequences are periodic zero-one sequences for the scheduling of packet transmissions in a time-slotted channel. A special class of protocol sequences, called shift-invariant sequences, plays a key role in achieving the information-theoretic capacity of the collision channel without feedback. This class of shift-invariant protocol sequences has the property that the pairwise Hamming crosscorrelation functions are invariant to relative delay offsets. However, the common period of shift-invariant sequences grows exponentially as a function of the number of supported users. In this paper, we consider a family of protocol sequences, whose period increases roughly as a quadratic function of the number of the users, and show that it is close to shift-invariant by establishing a bound on the pairwise Hamming crosscorrelation. The construction is based on the Chinese remainder theorem (CRT), and hence the constructed sequences are called CRT sequences. Applications to collision channel allowing successive interference cancellation at the receiver are discussed.