On Frame Asynchronous Coded Slotted ALOHA: Asymptotic, Finite Length, and Delay Analysis

TL;DR

This paper analyzes the performance of frame asynchronous coded slotted ALOHA (FA-CSA), showing it outperforms frame synchronous CSA in error floors, delay, and asymptotic thresholds, with detailed finite-length and delay analysis.

Contribution

It provides the first comprehensive analysis of FA-CSA, including asymptotic density evolution, finite-length error floor approximations, and delay performance, highlighting its advantages over FS-CSA.

Findings

FA-CSA achieves better error floor and waterfall performance than FS-CSA.

Boundary effects in FA-CSA improve the iterative decoding threshold.

FA-CSA exhibits superior delay properties compared to FS-CSA.

Abstract

We consider a frame asynchronous coded slotted ALOHA (FA-CSA) system for uncoordinated multiple access, where users join the system on a slot-by-slot basis according to a Poisson random process and, in contrast to standard frame synchronous CSA (FS-CSA), users are not frame-synchronized. We analyze the performance of FA-CSA in terms of packet loss rate and delay. In particular, 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 the receiver can monitor the system before anyone starts transmitting, a boundary effect similar to that of spatially-coupled codes occurs, which greatly improves the iterative decoding threshold. Furthermore, we derive tight approximations of the error floor (EF) for the finite frame length regime, based on the probability of occurrence of the most frequent stopping sets. We show that, in general, FA-CSA provides better performance in both the EF and waterfall regions as compared to FS-CSA. Moreover, FA-CSA exhibits better delay properties than FS-CSA.