Age of Information (AoI) measures the freshness of data in mission critical Internet-of-Things (IoT) applications i.e., industrial internet, intelligent transportation systems etc. In this paper, a new system model is proposed to estimate the average AoI (AAoI) in an ultra-reliable low latency communication (URLLC) enabled wireless communication system with decode-and-forward relay scheme over the quasi-static Rayleigh block fading channels. Short packet communication scheme is used to meet both reliability and latency requirements of the proposed wireless network. By resorting finite block length information theory, queuing theory and stochastic processes, a closed-form expression for AAoI is obtained. Finally, the impact of the system parameters, such as update generation rate, block length and block length allocation factor on the AAoI are investigated. All results are validated by the numerical results. Index Terms-Age-of-Information, finite block length regime, latency, reliability, ultra-reliable low latency communications (URLLC) and 5GB.

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Age of Information in an URLLC-enabled Decode-and-Forward Wireless
Communication System
Presentation · April 2021
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2. Age of Information in an URLLC-enabled
Decode-and-Forward Wireless Communication
System
Chathuranga M. Wijerathna Basnayaka †§, Dushantha Nalin K. Jayakody †§, Tharindu D.
Ponnimbaduge Perera † and Moises Vidal Ribeiro *
†National Research Tomsk Polytechnic University / §Center for Telecommunications
Research,SLTC,Sri Lanka/ * Federal University of Juiz de Fora Campus Universitario
The 2021 IEEE 93rd Vehicular Technology Conference: VTC2021-Spring,Helsinki,Finland
1 / 21

3. Outline
Outline
1 URLLC-enabled communication networks
2 Age of Information
3 System Model
4 Numerical Results
5 Conclusion
2 / 21

4. URLLC-enabled communication networks
URLLC-enabled communication networks
Ultra reliable low latency communications (URLLC)
So how do we optimally design URLLC systems ?
Morocho-Cayamcela, Manuel Eugenio, Haeyoung Lee, and Wansu Lim. ”Machine learning for 5G/B5G mobile and wireless
communications: Potential, limitations, and future directions.” IEEE Access 7 (2019)
3 / 21

5. URLLC-enabled communication networks
Fnite-blocklength information Theory
Large blocklengths mean large latency
Classic performance metric not suitable for the URLLC performances
Replace asymptotic information theory with nonasymptotic finite
blocklength ones!
The information theory community has developed many such
nonasymptotic results Ex : Polyanskiy Poor Verdú Converse Bound
4 / 21

6. Age of Information
Age of Information
Another approach to latency
Age of Information ( AoI ) measures the freshness of the received
data in mission critical applications.
Outdated information loses its value and can lead to system failures
and safety risks.
5 / 21

7. System Model
System Model
Figure: System model for URLLC-enabled relay system
6 / 21

8. System Model
System Model
The received signal at each node
Y1 =
p
PS HSRX1 + WSR (1)
Y2 =
p
PRHRDX2 + WRD (2)
PDF of the small scale channel gain (gij )
fgij (z) = e−z
(3)
Large scale channel gain αij
−10log(αij) = 20log(dij) + 20log
4πfc
C
(4)
7 / 21

9. System Model
System Model
Channel coefficient
Hij =
√
αij gij . (5)
Signal-to-Noise Ratio (SNR) γj at the receiving node j
γj =
αijgijPi
σ2
ij
(6)
8 / 21

10. System Model
Decoding Error Probability
The overall decoding error probability
ε = εR + εD(1 − εR) (7)
Following Polyanskiy’s results on short packet communication 1
εj = E
Q
nij C(γj ) − k
p
nij V (γj )
!#
(8)
1
Y. Polyanskiy, H. V. Poor, and S. Verdu, Channel coding rate in the Fnite blocklength regime,” IEEE Trans. Inf. Theory,
vol. 56, no. 5, pp. 230.
9 / 21

11. System Model
Decoding Error Probability
Under the Rayleigh fading channel conditions,
εj =
Z ∞
0
fγj (z)Q
nij C(γj ) − k
p
nj V (γj )
!
dz (9)
This can be approximated as
εj ≈
Z ∞
0
fγj (z)Θj(z) (10)
10 / 21

12. System Model
Θj (z) =



1, γj ≤ φj ,
1
2 − βj
√
nij (γj − ψj ), φj γj δj ,
0, γj ≥ δj ,
(11)
where βj = 1
2π
r
2
2k
nij −1
, ψj = 2
k
nij − 1, φj = ψj − 1
2βj
√
nij
and
δj = ψj + 1
2.βj
√
nij
.
The closed-form expression for the decoding error probability at the node
εij ≈ 1 −
βj
√
nij Pi αij
σ2
e
−
φi σ2
αij Pi − e
−
δj σ2
αij Pi
!
(12)
11 / 21

13. System Model
Decoding Error Probability
The closed-form expression for the overall error probability
ε ≈1 −
βRβD
√
nηSRηRD × ϕS ϕR(P)2αSRαRD
σ4
e
−
φR σ2
αSR ϕS P
− e
−
δR σ2
αSR ϕS P
e
−
φD σ2
αRD ϕR P
− e
−
δD σ2
αRD ϕR P
(13)
12 / 21

14. System Model
Average Age of Information
∆(t) = t − g(t) (14)
Figure: Evolution of Age of Information (∆(t)) with the time
13 / 21

15. System Model
Average Age of Information
The time average age
∆Tn =
1
Tn
Z Tn
0
∆(t)d(t) =
Pn−1
i=0 Qi
Tn
(15)
where
Qi =
Z Di +Xi
Di
∆(t)d(t) = Yi Xi +
1
2
X2
i
the AAoI can be written as
AAoI = ∆a =
E[X2]
2 + E[XY ]
E[X]
(16)
14 / 21

16. System Model
Average Age of Information
∆a =
1
2E
X2
E [X]
+ E [s] +
E [wX]
E [X]
(17)
Using Pollaczek–Khinchine formula 2,
E[wX] =
E[X](E[X] − E[s])
E[e−λs]
+
E[s2]E[X]
2(E[X] − E[s])
−
E[X2]
2
(18)
2
R. Talak, S. Karaman, and E. Modiano, “Can determinacy minimize ageof information?” arXiv preprint arXiv:1810.04371,
2018
15 / 21

17. System Model
Average Age of Information
Total number of transmission R
PR(m) = (1 − ε)εm−1
; m = 1, 2.... (19)
The transmission delay for an update
s = (nT + υ)R (20)
The AAoI of the proposed system
∆a =
(nT + υ)
1 − ε
+
(nT+υ)2(1+ε)
(1−ε)2
2(1
λ − (nT+υ)
1−ε )
+
(1
λ − (nT+υ)
1−ε )
(1−ε)e−(nT+υ)λ
1−εe−(nT+υ)λ
(21)
16 / 21

18. Numerical Results

19. Numerical Results
AAoI as a function of update generate
18 / 21

20. Numerical Results
AAoI as a function block length allocation factor
0.2 0.3 0.4 0.5 0.6 0.7 0.8
10-2
100
102
104
106
Power allocation factor - 0.5
Power allocation factor - 0.3
Power allocation factor- 0.7
19 / 21

21. Conclusion
Conclusion
Maintaining a small update size (short packet communication)
minimizes the AAoI in wireless relay networks
High packet generation rate may overload the network and lead to a
high average AoI
Low packet generation rate may result in infrequent information
updates at the destination, which may also lead to a high average AoI
20 / 21

22. Thank you
Contact:
• Email: chathurangab@sltc.ac.lk
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