Achieving Zero-Error Capacity 1 for a Collision Channel Without Feedback

TL;DR

This paper derives the zero-error capacity region for a collision channel without feedback using successive interference cancellation, showing that SIC can eliminate synchronization issues and achieve capacity 1 with appropriate protocol sequences.

Contribution

It extends the collision channel model by incorporating SIC, deriving the zero-error capacity region, and characterizing sequences needed for capacity 1.

Findings

Zero-error capacity region derived for the SIC-enabled collision channel.

SIC removes the negative impact of lack of synchronization on capacity.

Characterization of sequences achieving capacity 1 and their minimum period.

Abstract

The collision channel without feedback (CCw/oFB) model introduced by Massey and Mathys, depicts a scenario in which M users share a thermal noise-free communication channel with random relative time offsets among their clocks. This paper considers an extension of this model, which allows the receiver to use successive interference cancellation (SIC) to iteratively cancel the interference caused by those collided packets that have been decoded by the receiver. As the main result of this paper, we derive the zero-error capacity region of this channel in the slot-synchronous case, and present a zero-error capacity achieving scheme by joint protocol sequences and channel coding design. It is shown that the negative impact on the zero-error capacity due to a lack of time synchronization can be removed by the help of SIC. Moreover, we characterize the protocol sequences that can be used to achieve zero-error capacity 1 [packets/slot] by proving new results on shift-invariant sequences and throughput-invariant sequences; these sequences have been known to achieve zero-error capacity for the basic CCw/oFB model without SIC. This characterization sheds light on the minimum sequence period required in order to attain zero-error capacity 1.