On the Performance of Irregular Repetition Slotted ALOHA with an Age of Information Threshold Hooman Asgari

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On the Performance of Irregular Repetition Slotted ALOHA

with an Age of Information Threshold

Hooman Asgari

Technical University of Munich

Munich, Germany

hooman.asgari@tum.de

Andrea Munari

German Aerospace Center (DLR)

Wessling, Germany

andrea.munari@dlr.de

Gianluigi Liva

German Aerospace Center (DLR)

Wessling, Germany

gianluigi.liva@dlr.de

Abstract—The present paper focuses on an IoT setting in

which a large number of devices generate time-stamped updates

addressed to a common gateway. Medium access is regulated fol-

lowing a grant-free approach, and the system aims at maintaining

an up-to-date knowledge at the receiver, measured through the

average network age of information (AoI). In this context, we

propose a variation of the irregular repetition slotted ALOHA

(IRSA) protocol. The scheme, referred to as age-threshold IRSA

(AT-IRSA), leverages feedback provided by the receiver to admit

to the channel only devices whose AoI exceeds a dynamically

adapted target value. By means of detailed networks simulations,

as well as of a simple yet tight analytical approximation, we

demonstrate that the approach can more than halve the average

network AoI compared to plain IRSA, and offers notable im-

provements over feedback-based state-of-the-art slotted ALOHA

solutions recently proposed in the literature.

I. INTRODUCTION

Massive connectivity for the Internet of things (IoT) is

attracting a steadily increasing attention, and is envisaged to

become a key component of upcoming 6G wireless systems.

The possibility to gather data from a large population of low-

power, low-battery devices that generate trafﬁc in a sporadic

manner paves the way to a number of applications, ranging

among others from environmental and industrial monitoring

to asset tracking. In many of these settings, the ultimate goal

is to maintain an up-to-date perception of some monitored

processes at one or more collection points, e.g. to trigger

appropriate actuation steps.

Motivated by this remark, recent research efforts have

focused on the deﬁnition of strategies, often labeled as se-

mantic communications, that aim to facilitate delivery of the

right piece of information to the right point in time for IoT

applications [1]. To capture this ability, a number of new

performance metrics were introduced, ranging from age of

information (AoI) [2] to more advanced indicators such as

the age of incorrect information [3], the value of information

[4], [5], or the query AoI [6], [7].

Among these, AoI had a pioneering role. Originally pro-

posed for vehicular networks [8], [9], the metric quantiﬁes

the time elapsed since the generation of the freshest available

update on a tracked process. In spite of its simplicity, AoI has

A. Munari and G. Liva acknowledge the ﬁnancial support by the Federal

Ministry of Education and Research of Germany in the programme of

”Souver¨

an. Digital. Vernetzt.” Joint project 6G-RIC, project identiﬁcation

number: 16KISK022.

been shown to be an effective proxy to gauge the fundamental

trade-offs in a number of IoT and cyber-physical systems [5],

[10], and as such is of particular relevance. A good level

of maturity has been reached for the AoI behavior in point-

to-point communication links, see e.g. [10], [11] as well as

[2] and references therein. On the other hand, only recently

studies have started to focus on the implications of information

freshness in multi-access systems, spanning different layers of

the protocol stack [12]–[15].

From this standpoint, channel access strategies are of par-

ticular interest in the context of IoT connectivity. In fact, the

intermittent activity of a massive number of devices renders

traditional grant-based link-layer solutions ineffective, and

random access strategies based on variations of the ALOHA

paradigm [16] are commonly employed in practical systems

[17]. First fundamental results on the performance of such

schemes in terms of AoI have been obtained [18]–[22],

highlighting some speciﬁc design and optimization criteria to

target information freshness. In parallel, research has focused

on the study on a family of grant-free protocols designed in the

early 2000s, capable to go beyond the intrinsic throughput and

reliability limitations of the collision-beset ALOHA approach

[23]. These solutions, often dubbed modern random access,

allow nodes to proactively transmit multiple copies of a packet,

relying on successive interference cancellation at the receiver

side to resolve collisions, and have been shown to approach

performance competitive with that of coordinated access [24]–

[27]. Remarkable AoI improvements have also been recently

demonstrated for such schemes [28]–[30], prompting them as

promising candidates for IoT settings.

These lines of research typically focus on random access

settings that do not rely on feedback, assuming devices to

transmit without knowledge of the current AoI at the re-

ceiver. This hypothesis was relaxed by some notable works

in the past few years, which showed how the availability

of a return channel can dramatically improve performance

in slotted ALOHA [31]–[33]. In particular, the possibility to

prioritize channel access for nodes perceived by the sink as

stale by means of thresholding policies has proven capable to

approximately halve the average AoI with negligible losses in

terms of throughput.

The impact of feedback for the AoI of advanced grant-free

schemes remains to date instead largely unexplored. In this

arXiv:2210.15349v1 [cs.IT] 27 Oct 2022

paper we start to bridge this gap focusing on a modern random

access protocol, namely irregular repetition slotted ALOHA

(IRSA) [34]. We discuss the implications and costs of imple-

menting a feedback for such scheme, and propose a variation

of the algorithm, referred to as age-threshold IRSA (AT-IRSA),

which lets the receiver dynamically select a minimum level

of AoI required for nodes to contend. By means of detailed

network simulations we prove the remarkable beneﬁts of such

approach compared to the basic version of IRSA, especially for

large terminal populations. Furthermore, we present a simple

yet tight analytical approximation for the performance of the

scheme, and show that substantial improvements over some

state-of-the-art feedback-based slotted ALOHA policies [31],

[33] are attained.

II. SYSTEM MODEL AND PRELIMINARIES

Throughout our discussion we focus on a system composed

by a large number of terminals which share a common wireless

channel to communicate to a common receiver (also referred

to as sink, or monitor). Each of the Udevices becomes active

sporadically, attempting transmission of a time-stamped status

update, e.g., containing the reading of a monitored physical

process. In this setting, we aim to maintain a fresh and up-to-

date perception of the monitored processes at the receiver.

As customary in massive IoT applications, a random access

approach is implemented at the link layer, following a variation

of the irregular repetition slotted ALOHA protocol (IRSA)

described in details in Sec. II-A and III. In the remainder of

our discussion, we assume time to be divided in slots of equal

duration, and all devices to be synchronized to such pattern.

The transmission parameters are set such that a slot ﬁts a single

packet. Furthermore, following a well-established modeling

approach, we regard collisions as destructive. Accordingly, the

receiver cannot extract any information from a slot containing

the superposition of two or more packets. Conversely, a data

unit without interference (singleton slot) is always correctly

decoded. In addition, we assume the sink to be able to

differentiate among idle, singleton and collided slots.

A. Irregular Repetition Slotted ALOHA

Originally introduced in [34], IRSA is a grant-free scheme

designed to go beyond the intrinsic reliability and throughput

limitations of slotted ALOHA. The protocol operates over

frames of mslots each,1and the delivery of a packet can only

be initiated at the start over a new frame. Speciﬁcally, when

a terminal has data to send, it will transmit `copies of the

packet, uniformly distributed at random over the mavailable

slots in the upcoming frame. Each replica contains a pointer

to the positions in which its twins are sent.2The number of

copies is drawn from a pre-deﬁned distribution, shared by all

1Variations of the protocol operating over group of resources allocated in

a time-frequency thread are also possible, see, e.g. [35].

2This can be implemented by signaling the slots over which transmissions

are performed in the packet header. Alternative solutions to reduce overhead

are also possible, e.g. using the payload as seed for a random number

generator, used both at the sender and receiver side to place and locate replicas.

devices in the network. Following a well-established notation,

we specify such distribution in polynomial form as

Λ(x) =

`=1

Λ`x`

where Λ`is the probability to send `packet copies, up to a

maximum degree L.

At the sink, decoding relies on successive interference

cancellation (SIC) procedures. After buffering a whole frame,

the receiver starts by identifying singleton slots, which al-

low retrieval of non-collided packets. The incoming signal

contribution of each decoded data unit is then subtracted

from all the slots in which its copies were transmitted. This

interference cancellation procedure can thus potentially lead to

the identiﬁcation of additional singleton slots, and is iterated

until either all packets have been decoded or only slots with

collisions remain in the frame. An example of the described

receiver operation is reported in Fig. 1. In this case, 4users

access a frame of duration 5slots. Users 1,2and 3transmit

three copies of their packet, whereas user 4only sends two

replicas, leading to the initial conﬁguration of Fig. 1a. The

receiver starts by decoding user 3from slot 3(singleton), and

removes the contribution of such packet from slots 2and 4

(Fig. 1b). At this point, slot 4only contains the packet of user

1, which can be retrieved. Once more, the corresponding signal

is canceled from slots 1and 5, obtaining the conﬁguration of

Fig. 1c. Here, user 2is decoded from the ﬁrst slot, eventually

resolving all collisions involving user 4as well (Fig.1d).

To characterize the performance of IRSA in the remainder

of our discussion we resort to two key ﬁgures: channel load

and throughput. The former, denoted by G, captures the level

of contention over a frame. More precisely, let us introduce

the random variable (r.v.)

G`:= U`

describing the instantaneous channel load over the `-th frame,

where the r.v. U`indicates the number of terminals attempting

a transmission. The average channel load is accordingly

G=E[G`].

In turn, the throughput Sis deﬁned as the average number of

terminals decoded per slot The throughput behavior of IRSA

has been thoroughly studied in the literature, see e.g., [24],

[34], and an example of the achievable performance is reported

in Fig. 2 for a frame size m= 100 and an overall population

of U= 4000 users.

B. Age of Information: Preliminaries

To gauge the ability of a random access policy to maintain

a fresh perception of monitored processes at the sink, we

consider the age of information metric. Focusing without loss

of generality on an arbitrary terminal uin the system, let us

denote as δu(t)its instantaneous AoI, deﬁned as

δu(t) := t−σu(t)

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OnthePerformanceofIrregularRepetitionSlottedALOHAwithanAgeofInformationThresholdHoomanAsgariTechnicalUniversityofMunichMunich,Germanyhooman.asgari@tum.deAndreaMunariGermanAerospaceCenter(DLR)Wessling,Germanyandrea.munari@dlr.deGianluigiLivaGermanAerospaceCenter(DLR)Wessling,Germanygianluigi.liva@dlr...

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On the Performance of Irregular Repetition Slotted ALOHA with an Age of Information Threshold Hooman Asgari

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