Achieving Zero-Packet-Loss Throughput 1 for a Collision Channel Without Feedback and With Arbitrary Time Offsets

The collision channel without feedback (CCw/oFB) introduced by Massey and Mathys, depicts a scenario where multiple users share a communication channel but have arbitrary time offsets, and can never learn these time offsets due to the lack of feedback. This paper considers an extension of the CCw/oFB, which allows the receiver to use successive interference cancellation (SIC) to cancel the interference caused by those collided packets whose contents have been known by the receiver. We derive the zero-packet-loss throughput regions of this model for both the unsynchronized and slot-synchronized cases. Given an arbitrary number of users and a packet alphabet of arbitrary size, it is shown that these two regions coincide, and the outer boundary of this common region is the set of all points with only nonnegative components that add up to one. It is further shown that all points on this outer boundary with only rational components can be achieved without packet loss in the slot-synchronized case. The constructive proofs are based on a joint design of protocol sequences, identification/location algorithm and erasure correcting codes. These findings indicate that the negative impact of the lack of time synchronization on the throughput performance can be removed by the help of SIC.