Poisson Receivers: a Probabilistic Framework for Analyzing Coded Random Access

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.

ALOHA Receivers: a Network Calculus Approach for Analyzing Coded Multiple Access with SIC

“…To illustrate this, we provide a numerical example that uses two cooperative D-fold ALOHA receivers with packet coding to provide differentiated services between URLLC traffic and eMBB traffic. For D = 1, such a system is reduced to the CSA system with two cooperative receivers in [1]. The theoretical results in this example match extremely well with the simulation results (except for those data points with extremely small error probabilities).…”

“…In this section, we briefly review the framework of Poisson receivers in our previous work [1]. We say a system with K classes of input traffic is subject to a Poisson offered load ρ = (ρ 1 , ρ 2 , .…”

“…To hide the complexity from the physical layer, one needs an abstract model at the Medium Access Control (MAC) layer. Motivated by this, we proposed in our previous work [1] an abstract receiver, called Poisson receiver, that models the input-output relations of multiple classes of input traffic subject to an (independent) Poisson offered load. It was shown in [1] that various CSA systems in [6]- [10] can be modelled by Poisson receivers.…”

“…Motivated by this, we proposed in our previous work [1] an abstract receiver, called Poisson receiver, that models the input-output relations of multiple classes of input traffic subject to an (independent) Poisson offered load. It was shown in [1] that various CSA systems in [6]- [10] can be modelled by Poisson receivers. In this paper, we take one step further to show that the block fading channel with capture in [10], [20], [21] can also be modelled by Poisson receivers.…”

“…The rest of the paper is organized as follows. In Section II, we briefly review the framework of Poisson receivers in our previous work [1]. There we also show how to model the Rayleigh block fading channel with capture as a Poisson receiver.…”