Asymptotic and Finite Frame Length Analysis of Frame Asynchronous Coded Slotted ALOHA

TL;DR

This paper analyzes a frame-asynchronous coded slotted ALOHA system, deriving performance metrics and showing it outperforms the frame-synchronous version in error floors, thresholds, and delay, especially with system monitoring before transmission.

Contribution

It introduces an asymptotic analysis of FA-CSA, revealing boundary effects and providing finite-length error floor approximations, demonstrating performance improvements over FS-CSA.

Findings

FA-CSA has a higher decoding threshold than FS-CSA.

FA-CSA achieves lower error floors and better waterfall performance.

Monitoring before transmission enhances FA-CSA performance.

Abstract

We consider a frame-asynchronous coded slotted ALOHA (FA-CSA) system where users become active according to a Poisson random process. In contrast to standard frame-synchronous CSA (FS-CSA), users transmit a first replica of their message in the slot following their activation and other replicas uniformly at random in a number of subsequent slots. We derive the (approximate) density evolution that characterizes the asymptotic performance of FA-CSA when the frame length goes to infinity. We show that, if users can monitor the system before they start transmitting, a boundary-effect similar to that of spatially-coupled codes occurs, which greatly improves the decoding threshold as compared to FS-CSA. We also derive analytical approximations of the error floor (EF) in the finite frame length regime. We show that FA-CSA yields in general lower EF, better performance in the waterfall region, and lower average delay, as compared to FS-CSA.