Poisson Receivers: a Probabilistic Framework for Analyzing Coded Random Access

TL;DR

This paper introduces Poisson receivers, a probabilistic framework for analyzing coded random access systems, enabling exact throughput calculations and differentiated service analysis for diverse traffic types.

Contribution

The paper develops a novel Poisson receiver framework with closure properties, allowing analysis of complex coded access systems beyond classical methods.

Findings

Poisson receivers accurately model coded random access systems.

The framework enables exact throughput computation for systems with diversity.

Simulations confirm the theoretical predictions match real performance.

Abstract

In this paper, we develop a probabilistic framework for analyzing coded random access. Our framework is based on a new abstract receiver (decoder), called a Poisson receiver, that is characterized by a success probability function of a tagged packet subject to a Poisson offered load. We show that various coded slotted ALOHA (CSA) systems are Poisson receivers. Moreover, Poisson receivers have two elegant closure properties: (i) Poisson receivers with packet routing are still Poisson receivers, and (ii) Poisson receivers with packet coding are still Poisson receivers. These two closure properties enable us to use smaller Poisson receivers as building blocks for analyzing a larger Poisson receiver. As such, we can analyze complicated systems that are not possible by the classical tree evaluation method. In particular, for CSA systems with both spatial diversity and temporal diversity, we can use the framework of Poisson receivers to compute the exact (asymptotic) throughput. We demonstrate that our framework can be used to provide differentiated services between ultra-reliable low-latency communication (URLLC) traffic and enhanced mobile broadband (eMBB) traffic. By conducting extensive simulations, we also verify that our theoretical results match extremely well with the simulation results.