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arXiv:2401.10614v2 [cs.IT] 14 Jun 2024
1
Goal-Oriented Multiple Access Connectivity
for Networked Intelligent Systems
Pouya Agheli, Graduate Student Member, IEEE, Nikolaos Pappas, Senior Member, IEEE,
and Marios Kountouris, Fellow, IEEE.
Abstract—We design a self-decision goal-oriented multiple ac-
cess scheme, where sensing agents observe a common event and
individually decide to communicate the event’s attributes as up-
dates to the monitoring agents, to satisfy a certain goal. Decisions
are based on the usefulness of updates, generated under uniform,
change- and semantics-aware acquisition, as well as statistics and
updates of other agents. We obtain optimal activation probabilities
and threshold criteria for decision-making under all schemes,
maximizing a grade of effectiveness metric. Alongside studying
the effect of different parameters on effectiveness, our simulation
results show that the self-decision scheme may attain at least 92%
of optimal performance.
Index Terms—Goal-oriented multiple access, semantic update
acquisition, optimal activation probability, decision-making
I. INTRO DUC TI ON
GOAL -O RI ENT ED semantic communication holds great
promise for realizing resource-efficient and scalable net-
worked intelligent systems [1], where sensing agents observe
events and convey the events’ attributes to monitoring agents to
achieve a certain goal. Therein, update acquisition, data trans-
mission, and information usage become effective in satisfying
the goal when only useful or significant updates are considered
in the communication lifecycle. The challenge is exacerbated
when the medium is shared, and agents have to commu-
nicate over multiple access channels. Conventional medium
access protocols, such as typed-based ALOHA, grant-based,
and grant-free access, are primarily goal- and effectiveness-
agnostic, sending all frames regardless of their goal-dependent
usefulness and impact at the endpoint. Despite some prior
work [2]–[7], the problem of goal-oriented multiple access and
update provision remains mostly unexplored.
In this letter, we propose a self-decision goal-oriented mul-
tiple access scheme, in which each sensing agent decides
to speak up or remain silent based on the usefulness of its
generated updates and the statistics of the other agents and their
P. Agheli and M. Kountouris are with the Communication Systems De-
partment, EURECOM, Sophia-Antipolis, France, email: {pouya.agheli,
kountour}@eurecom.fr. M. Kountouris is also with the Department of
Computer Science and Artificial Intelligence, University of Granada, Spain.
N. Pappas is with the Department of Computer and Information Science,
Link¨oping University, Sweden, email: nikolaos.pappas@liu.se. The
work of P. Agheli and M. Kountouris has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (Grant agreement No. 101003431). The work of N.
Pappas has been supported by the Swedish Research Council (VR), ELLIIT,
and the European Union (ETHER, 101096526).
ISAk−1
ISAk
ISAK
NMAm−1
NMAm
NMAM
Event
Xn’s DTMC
X1X2
X2
X3
X3X4X5
1 2 3 In
p1,1
p1,In
pIn,1
MAC
MAC
MAC
...
Fig. 1. Goal-oriented medium access in a networked intelligent system.
generated updates for achieving a specific goal. The design
involves computing the optimal activation probabilities of the
agents and a decision-making criterion, which maximizes a
grade of effectiveness metric that integrates the discrepancy
error between actual and reconstructed events, the consumed
resources, and the usefulness of perceived updates. Our results
indicate that the proposed self-decision scheme is very close
to the optimal solution.
II. SY S TE M MO DE L
We consider Kintelligent sensing agents (ISAs) that ob-
serve a common event (information source) and convey their
noisy observations in the form of updates to Mnetworked
monitoring agents (NMAs) over a multiple access wireless
channel prone to errors and universal frequency reuse, c.f.,
Fig. 1. Communication occurs over independent time-slotted
service intervals. Within each interval, all NMAs query for
new observations from the ISAs in the downlink, and the ISAs
respond to those queries in the uplink, providing updates within
the same service interval. The evolution of the source Xtat the
t-th service interval, with t∈N, belongs to a finite state space.
An event at each state is described via a set of information
attributes, defined by A={Xn|n= 1,2,...,N}. Here,
Xn∈ {x(n)
i|i= 1,2,...,In}is a level-nattribute, which is
modeled by a discrete-time Markov chain (DTMC) with In≥2
states. In the DTMC modeling the n-th attribute, we assume
pi,i =p′
n, and pi,i′=pn,∀i6=i′, for i, i′= 1,2,...,In,
where p′
n+ (In−1)pn= 1.
At the t-th interval, the NMAs query for a group of attributes
b
At⊆ A represented by the sequence hb
Ati, where |b
At| ≤ N.
2
Either queried attribute is independently communicated in one
slot j,j= 1,2,...,|b
At|, with the same order as in hb
Ati.
The levels of queried attributes are determined in line with
the goal to which the NMAs subscribe. The k-th ISA, where
k= 1,2,...,K, can observe only a subset of attributes
Ak⊆ A and generate updates from its noisy observations via
an encoder, yielding a codebook shared with the other agents.
Moreover, Kn=hk:Xn∈ Akiis the sequence of ISAs that
can observe the n-th attribute. To estimate the event, the NMAs
need to jointly decode all queried attributes and construct b
Xt
at the t-th service interval. An attribute is correctly perceived
at that interval if at least MtNMAs successfully decode it,
where 1≤Mt≤M.
A. Goal-Oriented Update Provision
At the time slot order of the n-th queried attribute, the k-
th ISA, ∀k∈ Kn, generates an update from its observation
with probability βk,n , as obtained in Section IV-D, under the
following acquisition schemes [8]:
1) Uniform: An update is generated periodically at each
time slot, regardless of the prior state of the source and
the latest perceived update at the NMAs.
2) Change-aware: An update for an attribute is generated if
the state of that attribute changes at a time slot, regardless
of the latest perceived update.
3) Semantics-aware: Update generation for an attribute is
triggered once there is a discrepancy between the current
actual state of the attribute and that of the latest decoded
one of the same level at the NMAs. In this case, the ISAs
should maintain a record of the last decoded attributes.
The ISA follows a self-decision policy, thanks to which it
individually decides whether to transmit that update relevant
to the n-th attribute with probability αk,n . Each update is
assigned a meta value according to its usefulness in satisfying
the subscribed goal [9]. We consider v(n)
k,i ,∀k, i, n, the meta
value for the realization x(n)
iat the k-th ISA, and assume
it is assigned based on a knowledge fusion model, as in [9,
Section III-A]. In this work, the self-decision scheme takes the
form of a threshold-based decision policy. Thus, the k-th ISA
speaks up at the j-th slot if v(n)
k,j > v(n)
th,k; otherwise, it remains
silent. The threshold v(n)
th,k, shows a variable decision-making
criterion for the k-th ISA observing the n-th attribute.
B. Transmission Success Probability
As observations are noisy, updates generated from the same
event via different ISAs can be different, which leads to
signal contamination over the wireless network. We consider
hk,m =¯
hk,md−a
2
k,m the channel between the k-th ISA and the
m-th NMA, represented by an independent and identically dis-
tributed (i.i.d.) random variable (r.v.) where ¯
hk,m is the small-
scale fading with its power having a cumulative distribution
function (CDF) of Fh2(|¯
hk,m|2) = 1 −exp(−|¯
hk,m|2),dk,m
denoting the i.i.d. distance r.v.s, and 2≤a < 7being the
path-loss exponent. Let us consider γth the signal-to-noise ratio
(SNR) sensitivity. The probability of successful transmission of
the update from the k-th ISA and received at the m-th NMA is
γ(C,I)
k,m,n = PrSNR(C,I)
k,m,n > γth. The channel drop-off occurs
when SNR(C,I)
k,m,n ≤γth, with the probability of 1−γ(C,I)
k,m,n.
Here, Cshows the set of collaborating ISAs, and Iis that of
interfering ones. After some algebraic manipulations, we reach
γ(C,I)
k,m,n =X
k′∈CkX
k′′∈I "Qk′
0∈CkΛ(n)
k′
0,m Qk′′
0∈I Ω(n)
k′′
0,m
Λ(n)
k′,m +Ω(n)
k′′,m Λ(n)
k′,mΨ(n)
k,k′,k′′ ,m
×exp−Λ(n)
k′,mγth σ2
m#(1)
where Ck=C ∪ {k},Λ(n)
k′,m =da
k′,m
ρ(n)
k′,j
,Ω(n)
k′′,m =da
k′′,m
γthρ(n)
k′′,j
,
Ψ(n)
k,k′,k′′ ,m =Y
i∈Ck\{k′}
Λ(n)
i,m −Λ(n)
k′,m
×Y
j∈I\{k′′ }
Ω(n)
j,m −Ω(n)
k′′,m ,
σ2
mis the power of the complex additive white Gaussian noise
(AWGN) at the m-th NMA, and ρ(n)
k,j is the transmission power
of the k-th ISA for the n-th attribute at the j-th time slot.
III. PER FO RMA NC E METR ICS
We propose a grade of effectiveness (GoE) metric to evaluate
the effectiveness of communicated updates in the form of
GoE = ϕWT;g1(f1),...,gR(fR), which has R∈Z+
effectiveness features, with fr∈R+
0for r= 1,2,...,R
denoting the r-th one. Herein, W= [w1,...,wR]T∈RR,
0≤wr≤1, indicates a weight factor, where WT1R×1= 1.
Also, gr:R+
0→Ris a positive non-decreasing differentiable
function, and ϕ:R2R→Ris a context-dependent utility
function [1]. In this letter, we focus on three effectiveness
features to determine the GoE: Effective discrepancy error
(EDE), effective resource consumption (ERC), and effective
utility of updates (EUU).
A. Effective Discrepancy Error (EDE)
Update discrepancy error Etoccurs at the t-th service
interval if the actual event Xtis not equal to the reconstructed
b
Xt, i.e., Et=
1
{Xt6=b
Xt}. The EDE depicts the feature that
the effect of losing information is scaled by its usefulness in
satisfying the goal. Given this, we model the EDE as follows
EDE(Et,b
At;α
α
α, v) = F1X
n:Xn∈
b
At
Pe,n (2)
where F1=
|
b
At|
X
j=1 "X
k∈Kn
αk,nv(n)
k,j #n:Xn=Xj
,
3
α
α
α= [αk,n]K×N,v= [v(n)
k,j ]K×|
b
At|×N,Xj∈b
Atindicates the
attribute queried at the j-th time slot. We also have
Pe,n = lim
T→∞
1
T
T
X
t=1 PrE(n)
t,j = 1j:Xj∈
b
At
,(3)
which is the expected discrepancy error probability for the n-th
attribute and is derived according to Proposition 1. In (3), we
define E(n)
t,j =
1
{x(n)
j6=bx(n)
j|t}, and bx(n)
jshows the decoded
realization via the NMAs for the n-th attribute at the j-th slot.
Proposition 1. The expected discrepancy error probability Pe,n
for the n-th attribute is derived as
Pe,n =En(In−1)pn
1 + Enh2(In−1)pn−In−2
In−1pn−1i(4)
where En=1
2|Kn|P2|Kn|
ℓ=1 En,ℓ denotes the probability that the
n-th attribute is not successfully delivered to MtNMAs, where
En,ℓ =Y
k0∈R′
ℓ
(1−αk0,n )Y
k1∈¯
Rℓ
αk1,n
×
2|Rℓ|
X
τ=1 "Y
k2∈T ′
τ
(1−qk2,n )Y
k3∈Tτ
qk3,n Y
m∈Mk3
1−γ(Tτ,T′
τ)
k3,m,n #
(5)
where qk,n is the probability that the k-th ISA’s observation is
correct. Moreover, Rℓ,R′
ℓ,Tτ, and T′
τare the sets of ISAs that
are active, inactive, active with correct observations, and active
with incorrect observations, respectively. Also, Mk3shows the
subset of Mt+ 1 NMAs being farthest from the k3-th ISA.
Proof: We use the same approach as in [8, Section 3.2]
to derive (4). Considering its definition, the discrepancy error
E(n)
t,j ,∀t, j, n, follows a DTMC with two possible states {0,1}
and transition probabilities π(n)
a,b = PrE(n)
t+1,j′=b|E(n)
t,j =
a,∀a, b ∈ {0,1}, where Xj=Xj′=Xn. Therefore, we can
obtain the steady-state error probability Pe,n, as follows
Pe,n =π(n)
0,1
1 + π(n)
0,1−π(n)
1,1
.(6)
After computing π(n)
0,1and π(n)
1,1, we insert them into (6) and
obtain (4) after some algebraic manipulations.
B. Effective Resource Consumption (ERC)
The ERC feature allows us to model the resource con-
sumption for communicating updates as a function of its
usefulness. Having time-slotted channels with shared frequency
band, power is the main candidate resource to adapt. Therefore,
we define the transmission power of the k-th ISA at the j-th
time slot as ρ(n)
k,j =fρ(v(n)
k,i ), in the form of a non-decreasing
function fρ:R+
0→R+
0of the meta value assigned to x(n)
iat
the j-th slot. In this regard, we can write
ERC( b
At;α
α
α, v) = F2Y
n:Xn∈
b
At
Sn(7)
where F2=
|
b
At|
X
j=1 "X
k∈Kn
h αk,n
fρ(v(n)
k,j )
v(n)
k,j !#n:Xn=Xj
,
h:R+
0→R+
0is a non-decreasing differentiable function, and
Sn= 1 − Endenotes the probability of correctly delivering the
n-th attribute to the required number of NMAs.
C. Effective Utility of Updates (EUU)
The EUU feature shapes the utility (usefulness) of updates in
satisfying the goal once the actual event they are representing is
correctly reconstructed at the NMAs. Thereby, the EUU at each
service interval depends on the sum value of the communicated
attributes at that period, modeled as follows
EUU( b
At;α
α
α, v) = F1Y
n:Xn∈
b
At
Sn.(8)
IV. MULT IP L E ACC ESS DE SIG N
We aim to design a multiple access scheme via obtaining
the set of optimal activation probabilities α
α
α∗= [α∗
k,n]K×N,
maximizing the GoE in the system based on the goal. Next,
we find the threshold criteria for decision-making and propose
a self-decision scheme under all update acquisition schemes.
A. Problem Formulation
Based on Section III, we formulate the problem as follows
P1:max
α
α
α,WGoE = ϕWT;g1(f1),...,gR(fR)
s.t. 0α
α
α1,0≺W1,WT1R×1= 1.(9)
Without loss of generality, we transform the GoE optimiza-
tion in P1to a problem of minimizing the weighted sum of the
EDE and ERC features, named G, subject to guaranteeing that
the EUU exceeds a minimum value denoted by EUUmin at each
service interval. As transmissions are performed independently
among the service intervals, it is sufficient to analyze the
effectiveness problem for an arbitrary t-th period. Then, we can
apply the same access design for the other periods, depending
on b
At,∀t. Therefore, we can write
P2:min
0α
α
α1,0≺W1G=
2
X
r=1
wrgr(fr)
s.t. g3EUU( b
At;α
α
α, v)≥EUUmin,WT13×1= 1 (10)
where f1= EDE(Et,b
At;α
α
α, v), and f2= ERC( b
At;α
α
α, v).
B. Problem Solution
Inserting (2), (7), and (8) into (10), we define the Lagrange
function Lfor P2, and we can write the Karush-Kuhn-Tucker
(KKT) conditions, as follows
∂L
∂αk,n
=
4
w1"F1∂Pe,n
∂αk,n +Pe,n ∂F1
∂αk,n #g′
1
F1X
n:Xn∈
b
At
Pe,n
+w2Sn"Sn∂F2
∂αk,n +F2∂Sn
∂αk,n #g′
2F2SnSn
−ηSn"Sn∂F1
∂αk,n +F1∂Sn
∂αk,n #g′
3F1SnSn
+λk,n = 0,∀k, n, (11)
where Sn=Qn′∈
b
At\{Xn}Sn′. Moreover, we have
∂L
∂w1
=g1
F1X
n:Xn∈
b
At
Pe,n
+µ0+µ1= 0,(12)
∂L
∂w2
=g2F2SnSn+µ0+µ2= 0.(13)
In (11)–(13), η≥0,µr≥0,∀r, and λk,n ≥0,∀n:Xn∈b
At,
∀k∈ Kn, denote Lagrange multipliers.
The complementary slackness conditions are as below
H1:ηg3F1SnSn−EUUmin= 0,
H2:µr(wr−1)= 0, r = 1,2,H3:λk,n (αk,n −1) = 0,∀k , n.
Each of H1to H3holds under two conditions: In H3, we
consider (i) λk,n = 0, hence αk,n <1; or (ii) αk,n = 1, thus
λk,n >0. Under condition (ii), the ISAs are active at all time
slots, which is not optimal according to (4). Thus, we reach
λk,n = 0,∀k, n. In H2, we assume (i) µr= 0, then wr<1;
or (ii) wr= 1, hence µr>0. Condition (ii) leads one of the
weighting variables to become zero, which is incorrect referring
to P2. Thus, we have µr= 0,∀r. Given this, we arrive
F2=1
SnSn
g−1
2
g1
F1X
n:Xn∈
b
At
Pe,n
.(14)
Also, for H1, we have (i) η= 0, and g3F1SnSn>EUUmin;
or (ii) g3F1SnSn= EUUmin, and η > 0. Applying (14)
into (11), condition (i) results in negative probabilities. Thus,
condition (ii) is true with g3F1SnSn= EUUmin. From (11),
we obtain
Pe,n =
g−1
1ηSnSnEUUmin
2w1
F1Pn′:Xn′∈
b
At\{Xn}Pe,n′
1/2
.(15)
Putting together (4), (5), and (15), and after some simple
numerical and algebraic manipulations based on the forms of
g1,h, and fρ, the optimal α∗
k,n,∀k , n, is derived. We achieve
optimal w∗
1and w∗
2by exerting α
α
α∗into the Lagrange function
and equalizing the equation L(W) = L(α
α
α∗). In this regard,
Algorithm 1 is proposed, which provides the optimal values
for the optimization variables with certain stopping accuracy
and convergence rate of O((NiNj)−1), where Niand Njare
the maximum numbers of inner and outer loops, respectively.
Algorithm 1: Solution for deriving α
α
α∗and W∗at the
t-th service interval.
Input: Known parameters M,L,p,b
At,Kn,v(n)
k,j ,∀j, k,
qk,n,γ(C,I)
k,m,n,∀n, k,EUUmin,ε1
ε1
ε1, and ε2
ε2
ε2. Initial
parameters η(0) ←0,α
α
α(0) =0K×|
b
At|, and
W= [0.5,0.5]T. Forms of gr,∀r,h, and fρ.
Output: Optimal parameters α∗
k,n,∀k , n,w∗
1, and w∗
2.
1Iteration j:⊲Outer loop
2if conditions H4to H6are met. then goto 3.
3Iteration i:⊲Inner loop
4Consider n=hb
At(c)ic=1 and k=hKn(c)ic=1.
5Update S(i)
n,F(i)
1,F(i)
2(α
α
α), and P(l,i)
e,n′,∀n′∈b
At\ {n}.
6Derive α∗
k,n from (4), (5), (15), and given αk′,n,
∀n, k′∈ Kn\ {k}; update and save α
α
α(i).
7goto 4and repeat for hb
At(c)i|
b
At|
c=2 and hKn(c)i|Kn|
c=2 .
8if α
α
α(i)−α
α
α(i−1)> ε1
ε1
ε1then set i=i+1, and goto 3.
9Compute w(j)
1and w(j)
2; save W(j).
10 if W(j)−W(j−1)> ε2
ε2
ε2,W(j)0,W(j)1, or
∃k,nα(i)
k,n <0then step up η(j),j=j+1, and goto 1.
11 Return α
α
α∗=α
α
α(i)and W∗=W(j).
Remark 1. The convexity of Lrelies on the forms of g1,g2,
and g3. For convex g1and g2but concave g3, the dual problem
is definitely convex with the following conditions
H4:∂F1
∂αk,n
∂Pe,n
∂αk,n
+F1
2
∂2Pe,n
∂α2
k,n
≥0,
H5:∂Sn
∂αk,n
∂F2
∂αk,n
+Sn
2
∂2F2
∂α2
k,n
≥0.
For all being convex, Lis convex if H4,H5, and H6hold, with
H6:ηF1
∂Sn
∂αk,n
+Sn
∂F1
∂αk,n g′′
3F1SnSn
≤w2F2
∂Sn
∂αk,n
+Sn
∂F2
∂αk,n g′′
2F2SnSn.(16)
The reverse of Remark 1 is not necessarily true. Exerting
(7), (14), and Remark 1, optimal forms of hand fρare found.
C. Analysis for Large In
We consider Xn,∀n, has large enough state space, i.e., In≫
1. In this regime, we achieve lim
In→∞Pe,n =1
2from (4). Besides,
we rewrite (5) and define E(k)
nand b
E(k)
nas below
E(k)
n=Pℓ:k∈RℓEn,ℓ
αk,n
,b
E(k)
n=Pℓ:k∈R′
ℓEn,ℓ
1−αk,n
.
Thereby, using (15), α∗
k,n,∀k , n, is derived as follows
α∗
k,n =
ηSnEUUmin1−b
E(k)
n−2w1g1
F1
2(|
b
At|+1)
ηSnEUUminE(k)
n−b
E(k)
n.(17)
5
From (17), we infer that α∗
k,n increases by (i) decreasing the
average usefulness of updates to tackle the high contamination
of useful updates over the channels, (ii) enlarging the set of
queried attributes, and (iii) increasing the EUUmin constraint.
D. Decision Making Criterion
To obtain the threshold criterion v(n)
th,k,∀k,∀n∈ Ak, for the
self-decision scheme proposed in II-A, the k-th ISA needs to
timely compute α∗
k,n,∀k, n, according to Section IV-B. To this
end, the ISA measures its distance from all NMAs thanks to
the received query signals and has knowledge of Kn, the other
ISAs’ location distribution, update usefulness distributions, and
observation accuracy. We derive the following upper bound for
γk,m,n in (1) by applying the Markov’s inequality
γ(C,I)
k,m,n ≤E
Ck
X
k′∈CkX
k′′∈I Qk′
0∈CkΛ(n)
k′
0,m Qk′′
0∈I Ω(n)
k′′
0,m
Λ(n)
k′,m +Ω(n)
k′′,m Λ(n)
k′,m3Ω(n)
k′′,m
.
(18)
After equalizing γ(C,I)
k,m,n to its upper bound and using Algo-
rithm 1, α∗
k,n is derived for the k-th ISA and n-th attribute at
any arbitrary service interval. Eventually, we arrive
v(n)
th,k =F−1
V 1−min(1,α∗
k,n
max0, βk,n)! (19)
where FV(v(n)
k,j )indicates the CDF of the update’s meta value.
Also, βk,n shows the scheme-dependent probability that the
k-th ISA generates updates for the n-th attribute, given by
βk,n =
1; uniform
(In−1)pn;change-aware
Pe,n(1−Inpn) + (In−1)pn;semantics-aware
(20)
if k∈ Kn; otherwise, βk,n = 0.
V. SI MU L ATION RE SULTS
We investigate the performance of the proposed self-decision
scheme for satisfying the goal with EUUmin = 0.1. We
consider K= 10,M= 4,In= 10,p′
n= 0.2,∀n,|b
At|= 10,
Mt=⌈M+1
2⌉= 3,∀t, and qk,n = 0.8,∀k, n. We also
randomly select a subset of the ISAs constructing Kn,∀n.
Additionally, we assume that the distance between each pair
of ISA and NMA having a 7 [m]height follows a standard
normal distribution with standard deviation 60 [m], the path-loss
exponent a= 3.8,σ2
m=−120 [dBm], and γth = 10 [dB]. The
assignment of a meta value to each update is based on a beta
distribution with both shape parameters equal to 2. Moreover,
g1,g2, and g3have exponential forms, while hand fρare
linear and cubic functions, respectively. To simplify, we assume
αk,n =αk′,n′and accordingly v(n)
th,k =v(n′)
th,k′,∀n, n′, k, k′.
Fig. 2 illustrates the effect of the meta value threshold, i.e.,
v(n)
th,k,∀n, k , hence activation probability, on the effectiveness.
The optimization objective of the effectiveness problem, i.e.,
Fig. 2. The objective of P2and its constraint versus the meta value threshold.
Fig. 3. The interplay between the objective of P2and the number of states
in the DTMC for different sizes of required attributes.
Gin P2, and its EUU constraint are plotted versus v(n)
th,k based
on different update acquisition schemes and W= [0.5,0.5]T
using Monte Carlo simulations with 500 iterations. Despite al-
most identical G, the semantics-aware scheme offers the highest
EUU on average. To satisfy EUUmin, as shown in Fig. 2, the
semantics-aware, uniform, and change-aware schemes require
transmission rates of αk,n = 0.6,0.61, and 0.62,∀k, n,
respectively, under the first root, while they generate updates
with rates of 0.91,1, and 0.8. Thus, we infer that the semantics-
aware scheme poses, averagely, 6.4% less channel load than the
uniform scheme and 5% more than the change-aware one.
To assess the self-decision scheme, we apply Algorithm 1
to derive the set of optimal activation probabilities based on
different schemes and the assumed W. In this case, we reach
αk,n = 0.64,0.64, and 0.67,∀n, k , for the semantics-aware,
uniform, and change-aware schemes, respectively. Compared to
the derived values from Fig. 2, the accuracy of the self-decision
scheme is more than 92%. More importantly, EUUmin is not
satisfied without our self-decision scheme.
The interplay between Gand the number of states in the
DTMC, i.e., In,∀n, is depicted in Fig. 3 based on different
values of |b
At|,∀t. Therein, we plot the lowest value of the
objective that meets EUUmin . We see that increasing Inresults
in higher Gdue to the increase of Pe,n and EDE, accordingly,
concerning (4). Additionally, higher values of |b
At|boost ERC
according to (7), leading to higher G. Thus, the fewer attributes
queried within a service interval, the higher the effectiveness.
6
VI. CO NCL USI ON
We developed a self-decision goal-oriented multiple access
scheme for networked intelligent systems. Aiming to maximize
the GoE, we obtained the optimal activation probabilities and
threshold criteria for decision-making under different update
acquisition schemes. Analyzing how different parameters affect
the effectiveness, our simulation results showed that our pro-
posal could achieve at least 92% of the optimal performance.
REF ERE NC ES
[1] M. Kountouris and N. Pappas, “Semantics-empowered communication for
networked intelligent systems,” IEEE Comm. Mag., vol. 59, no. 6, 2021.
[2] G. Mergen and L. Tong, “Type based estimation over multiaccess chan-
nels,” IEEE Trans. Signal Process., vol. 54, no. 2, 2006.
[3] L. Liu, E. G. Larsson, W. Yu, P. Popovski, C. Stefanovic, and E. De Car-
valho, “Sparse signal processing for grant-free massive connectivity: A
future paradigm for random access protocols in the Internet of Things,”
IEEE Signal Process. Mag., vol. 35, no. 5, 2018.
[4] Y. Wu, X. Gao, S. Zhou, W. Yang, Y. Polyanskiy, and G. Caire, “Mas-
sive access for future wireless communication systems,” IEEE Wireless
Commun., vol. 27, no. 4, 2020.
[5] A. Munari, “Modern random access: An age of information perspective
on irregular repetition slotted ALOHA,” IEEE Trans. Commun., vol. 69,
no. 6, 2021.
[6] J. Choi, J. Ding, N.-P. Le, and Z. Ding, “Grant-free random access in
machine-type communication: Approaches and challenges,” IEEE Wireless
Commun., vol. 29, no. 1, 2021.
[7] S. Daei and M. Kountouris, “Blind goal-oriented massive access for future
wireless networks,” IEEE Trans. Signal Process., vol. 71, 2023.
[8] N. Pappas and M. Kountouris, “Goal-oriented communication for real-time
tracking in autonomous systems,” in IEEE ICAS, 2021.
[9] P. Agheli, N. Pappas, and M. Kountouris, “Semantic filtering and source
coding in distributed wireless monitoring systems,” IEEE Trans. Commun.
(Early Access), 2024.
