TELKOMNIKA Telecommunication Computing Electronics and Control Vol.
No.
April 2026, pp.
ISSN: 1693-6930.
DOI: 10.
12928/TELKOMNIKA.
Secure two-way relaying with successive interference cancellation and fountain codes: performance analysis Nguyen Thi Hau1,2.
Tran Trung Duy3 Department of Electronics and Telecommunication Faculty of Electronics Technology.
Industrial University of Ho Chi Minh City.
Ho Chi Minh City.
Vietnam Faculty of Engineering and Technology.
Saigon University.
Ho Chi Minh City.
Vietnam Faculty of Telecommunications 2.
Posts and Telecommunications Institute of Technology.
Ho Chi Minh City.
Vietnam
Article Info
ABSTRACT
Article history:
This paper proposes a secure two-way relaying (TWR) scheme using fountain codes (FC.
, successive interference cancellation (SIC), and digital network coding (DNC).
Using FCs, two sources exchange their data by first encoding the data into a series of packets .
alled encoded packet.
These encoded packets are then exchanged between the sources via the help of a common relay, and they are also overheard by an eavesdropper.
The packet exchange is carried out over two time slots: .
in the first time slot, both sources send their encoded packets to the rela y.
and i.
the relay applies SIC to decode two received packets, and then broadcasts the exclusive OR (XORe.
packet to both sources in the second time slot.
The sources and the eavesdropper try to collect a sufficient number of encoded packets to successfully recover the original data.
This paper derives and validates exact closed-form expressions for system throughput (TP), system outage probability (SOP), and system intercept probability (SIP) over Rayleigh fading channels.
Furthermore, our findings reveal a reliability-security tradeoff as well as the impact of system parameters on the network performance.
Received Apr 12, 2025 Revised Dec 1, 2025 Accepted Dec 8, 2025 Keywords:
Digital network coding Fountain codes Interference cancellation Physical layer security Two-way relaying This is an open access article under the CC BY-SA license.
Corresponding Author:
Nguyen Thi Hau Faculty of Engineering and Technology.
Saigon University 273 An Duong Vuong Street.
Cho Quan Ward.
Ho Chi Minh City.
Vietnam Email: hau.
nt@sgu.
INTRODUCTION
Recently, two-way relaying (TWR) .
has emerged as an effective technique for enhancing both data throughput and coverage in next-generation wireless communication systems.
In TWR scheme, one or many intermediate relays assist the exchange of data between two source nodes .
In the conventional TWR scheme, 04 phases are used to exchange 02 packets between two sources.
The researches .
, .
combined digital network coding (DNC) and decoding and forward (DF) relaying to reduce 1 phase, resulting in data exchange occurring in 03 phases.
In these schemes, two source nodes send their packets to the relay in the first two phases, the relay performs exclusive OR (XOR) operation on two encoded packets in the third phase, and broadcasts the XORed packet to both sources.
Unlike the schemes proposed in .
the TWR scheme in this work uses only two phases.
Indeed, the relay nodes in .
employ successive interference cancellation (SIC) to decode the received packets at the first phase, and forward the packets to two sources in the second phase.
Huynh et al.
, relay selection techniques were employed to enhance performance for the TWR schemes, while Dao and Son .
proposed the TWR schemes using energy harvesting (EH).
Additionally, the authors in .
, .
explored reconfigurable intelligent surfaces (RIS) Journal homepage: http://journal.
id/index.
php/TELKOMNIKA TELKOMNIKA Telecommun Comput El Control working as a common relay to improve the spectral efficiency of two-way communication.
However, the previous works .
did not consider fountain codes (FC.
and physical-layer security (PLS).
Due to the broadcast of wireless channels, ensuring secure communication has become a critical challenge in the TWR networks.
To achieve secure communication.
PLS which exploits the natural characteristics of wireless channels such as fading, interference, and noise can be effectively applied to the TWR networks .
Cai et al.
, proposed a randomize and forward (RanF) technique, where two source and relay nodes transmit different codewords to limit the overhearing ability of the eavesdropper.
Liu et al.
introduced a secure amplify-and-forward (AF) TWR scheme-aided simultaneous wireless information and power transfer (SWIPT) technique where multi-antenna source and relay nodes operate in the full-duplex mode.
Luo et al.
, the PLS TWR models using intelligent reflecting surfaces (IRS) were proposed and analyzed.
Recently, the integration of error correction codes (ECC) and PLS to simultaneously enhance security and performance has emerged as a promising solution in wireless communication .
Following these approaches.
FCs, known for their rateless property, offer significant advantages such as adaptability to dynamic channel conditions, simplified coding and decoding protocols, and robustness against packet loss, making them attract more attention in recent studies .
, .
To reconstruct the original data, receivers have to sufficiently collect encoded packets .
, .
According to .
, .
, achieving data security requires that legitimate users or destinations collect a sufficient number of encoded packets before Nguyen .
analyzed the reliability-security trade-off (RST) in the secure TWR networks between two clusters of nodes using DNC.
Unlike the authors in .
, .
proposed TWR CR schemes that incorporate FCs.
RIS, and wireless EH, where RIS can replace a relay node to facilitate data exchange between two source nodes.
To the best of our knowledge, the work in .
is the study most closely related to our work.
While .
investigated a SIC-DNC-based TWR network employing FCs, its analysis was limited to the outage performance and therefore focused exclusively on the reliability of the system.
However, modern wireless networks require not only high reliability but also robustness against eavesdropping threats .
Unlike .
, this paper extends the research by integrating a passive eavesdropper into the system model and conducting a comprehensive joint evaluation of reliability and security performance.
In the proposed scheme, two source nodes exchange encoded packets via a DF relay in two time slots, while an eavesdropper attempts to During the first time slot, both sources transmit encoded packets to the relay, which employs SIC to decode the received packets.
Then, the relay performs XOR on these packets and broadcasts the XORed packet to both sources in the second time slot.
If two source nodes collect a sufficient number of encoded packets, they can reconstruct the desired data.
Also, if the eavesdropper can correctly recover the original data, the data of the two sources is intercepted.
We derive closed-form expressions for SOP and SIP, evaluate the reliabilityAesecurity trade-off, and demonstrate how system parameters such as relay position, power allocation factor, and the maximum number of transmission times influence overall system performance.
This comprehensive analysis offers deeper insights into the advantages that FCs introduce to the secure SICDNC-based TWR network that has not been explored in .
The remainder of the paper is organized as follows: section 2 presents the system model and scheme operation.
section 3 analyzes performance.
provides simulation and theoretical results.
and section 5 concludes with a summary and future directions.
SECURE TWR WITH SIC AND FCs System model In the proposed scheme presented in Figure 1, since there exists no direct communication between two source nodes S1 and S2 due to the far distance.
S1 and S2 have to exchange their data with the assistance of the relay (R) In the network, the eavesdropper (E) attempts to overhear the data sent from ycI1 and ycI2 .
All of the nodes are equipped with a single antenna and operate in a half-duplex mode.
Let us denote ycu1 .
cu2 ) as the data sent from ycI1 .
cI2 ), and ycy1 .
cy2 ) as encoded packets of ycI1 .
cI2 ), respectively.
Before transmission data takes place, ycI1 .
cI2 ) divides ycu1 .
cu2 ) into small packets, then perform XOR operation on these packets to continuously generate Fountain packets ycy1 .
cy2 ).
The exchange of encoded packets in the proposed scheme occurs in two time slots.
At the first time slot, both S1 and S2 simultaneously send ycy1 and ycy2 to R.
Then.
R uses SIC technique to decode ycy1 and ycy2 .
If both ycy1 and ycy2 are decoded correctly.
R performs the XOR operation over ycy1 and ycy2 to make ycyA , where ycyOi = ycy1 Oi ycy2 .
In the second time slot.
R broadcasts ycyA to ycI1 and ycI2 .
If R only decodes ycy1 .
r ycy2 ) successfully, it only transmits ycy1 .
r ycy2 ) to ycI2 .
r ycI1 ) in the second time slot.
Let yamin denote the number of encoded packets that S1 .
S2 , and E need to obtain for reconstructing the data ycu1 and ycu2 .
Let yamax denote the maximum number of transmissions of ycI1 and ycI2 , where yamax Ou yamin .
We also denote yccXY and yu as the distance between X and Y, and path-loss exponential, respectively.
Secure two-way relaying with successive interference cancellation and fountain A (Nguyen Thi Ha.
A ISSN: 1693-6930 where X.
Y OO {S1 .
S2 .
E}.
Let denote yua02 as variance of Gaussian noises at all receivers.
Finally, ycES1 , ycES2 , and ycER are denoted as transmit power of S1 .
S2 , and R, respectively.
pEI p1 / pEI pEI Data link Eavesdropping link Figure 1.
The proposed secure TWR scheme using FCs and SIC Assume that all channels are block Rayleigh fading, where channel coefficients remain constant during one time slot, and change independently after each time slot.
Let EaXY and yciXY = |EaXY .
denote channel coefficient and channel gain of between ycU and ycU, respectively.
As in studies .
, yciXY has cumulative distribution function (CDF) and probability density function (PDF), respectively as:
yayciXY .
= 1 Oe yceycuycy(OeyuIXY yc.
, yceyciXY .
= yuIXY yceycuycy(OeyuIXY yc.
where yciXY = .
ccXY )yu .
In practical scenarios, implementing such secure TWR schemes may face challenges related to hardware limitations, latency, and energy efficiency, which can affect real-time system performance.
Moreover, the proposed secure TWR scheme can be extended to future 6G and IoT networks, where EH and hardware impairments (HI.
become important factors for practical deployment.
However, in this study, we focus on analyzing the secure TWR scheme using SIC and FCs under ideal SIC conditions and without considering energy constraints or HIs at the nodes.
These aspects are left for future research to evaluate their impact on the systemAos secrecy and reliability performance.
Transmit power formulation and transmission of encoded packets For a fair comparison between our scheme .
amed SIC-2TS) and the conventional DNC scheme .
amed DNC-3TS), we assume that the total transmit power in two schemes is the same, i.
ycEycI1 ycEycI2 = 2ycE, ycEycI = ycE Note that the transmit power of ycI1 , ycI2 and R in the DNC-3TS scheme is ycEycI1 = ycEycI1 = ycEycI = ycE.
Moreover, we propose a simple power allocation method for .
as follows:
ycEycI1 = 2yuycE, ycEycI1 = 2.
Oe y.
ycE .
where yu is a pre-designed power allocation factor and 0 < yu < 1.
Oe Remark 1: without loss of generality, we can assume ycI1 is nearer ycI than ycI2 , i.
, yccycI1 ycI < yccycI2 ycI .
Hence, we can assume that the ycI1 Ie ycI channel is better than the ycI2 Ie ycI, and hence, ycI uses SIC to decode ycy1 first, treating the signal from ycI2 as interference.
After cancelling ycy1 , ycI decodes ycy2 .
In the first time slot, ycI1 and ycI2 at the same time transmit their packets to ycI.
The signal-tointerference-plus-noise ratio (SNR) obtained at ycI for decoding ycy1 and ycy2 , can be expressed, respectively as .
TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 420-430 TELKOMNIKA Telecommun Comput El Control ycEycI1 yciycI1 ycI yuycISIC-2TS 1 IeR,ycy1 where yuu = ycE yua02 ycEycI2 yciycI2 ycI yua02 2yuyuuyciycI1 ycI 2.
Oey.
yuuyciycI2 ycI 1 , yuycISIC-2TS 2 IeR,ycy2 ycEycI2 yciycI2 ycI yua02 = 2.
Oe y.
yuuyciycI2 ycI .
Then, the corresponding channel capacity obtained at ycI can be given, respectively as:
yaycISIC-2TS = ycoycuyci2 .
yuycISIC-2TS ) , yaycISIC-2TS = ycoycuyci2 .
yuycISIC-2TS 1 IeR,ycy1 1 IeR,ycy1 2 IeR,ycy2 2 IeR,ycy2 .
where the factor 1/2 implies that the packet exchange is carried out over two time slots.
Similar to R, ya also employs SIC to detect ycy1 and ycy2 in the first time slot.
Hence, the instantaneous channel capacity obtained at ya to decode ycy1 and ycy2 can be expressed, respectively, as:
2yuyuuyciycI1 ya 2.
Oey.
yuuyciycI2 ya 1 yaycISIC-2TS = ycoycuyci2 .
1 IeE,ycy1 ) , yaycISIC-2TS = ycoycuyci2 .
Oe y.
yuuyciycI2 ya ).
2 IeE,ycy2 .
Oe Remark 2: we also assume that yccycI1 ya < yccycI2 ya , and similar to ycI, ya will decode ycy1 first.
Note that if yccycI1 ya Ou yccycI2ya , the IP/SIP performance at ya is worse than those with yccycI1 ya < yccycI2 ya .
Next, assume that the packet ycy ycyycn .
cn = 1,.
can be correctly decoded by ya.
a OO {R,E}) if yaya ycn Ou yath , where yath is an outage threshold.
ycyycn yaya < yath , the decoding of ycyycn at ya fails.
Hence, there are three possible cases regarding the decoding status at ycI as follows:
Case 1: if ycI can correctly decode both ycy1 and ycy2 , and it then broadcasts ycyOi to both ycI1 and ycI2 in the second time slot.
Therefore, the capacity of the ycI Ie yaA links .
aA OO .
cI1 , ycI2 , y.
) can be formulated as:
SIC-2TS
yaycIIeB,ycy = ycoycuyci2 .
yuuyciRB ) Oi Case 2: if ycI can only decode ycy1 correctly, it will transmit ycy1 to ycI2 in the second time slot.
In this case, the channel capacity of the ycI Ie ya links .
a OO .
cI2 , y.
) links can be given as:
SIC-2TS
yaycIIeC,ycy = ycoycuyci2 .
yuuyciRC ) .
Case 3: in this case, ycI cannot decode both ycy1 and ycy2 , and there is no transmission at the second phase.
Next, we consider the DNC-3TS scheme, where each packet exchange is performed via three time slots: .
ycI1 transmits ycy1 to ycI at the first time slot.
ycI2 transmits ycy2 to ycI at the second time slot.
ycI broadcasts ycyOi to ycI1 and ycI2 at the third time slot.
It is also worth noting that if ycI only decodes ycy1 or ycy2 correctly, it will send ycy1 .
cy2 ) to ycI2 .
cI1 ) at the third time slot.
Therefore, we can formulate the channel capacity obtained at the node ycU, due to the transmission of the packet ycyO of the node ycU, as follows:
DNC-3TS
yaycUIeycU,ycy = ycoycuyci2 .
yuuyciXY ).
where ycyO OO .
cy1 , ycy2 , ycyOi }.
PERFORMANCE EVALUATION
This section derives exact closed-form expressions of system throughput (TP).
SOP and SIP for the SIC-2TS and DNC-3TS schemes.
Now, we will calculate the probability that the node yaA in SIC-2TS and DNC-3TS can correctly receive one encoded packet ycyycn .
Decoding probability of one encoded packet In SIC-2TS, the probability that one packet ycy1 is successfully reached to ycI2 can be formulated as:
SIC-2TS
A SSIC-2TS
= Pr ( CSSIC-2TS
Ie R,p C Cth ) Pr ( CR IeS ,p C Cth ) = Pr ( gS R C A1 gS R A0 ) Pr ( g RS C A 2 ) = EE
EE 0
Oe F ( A x A )) f gS1R gS2R ( x ) dx e .
Oe FRS ( A2 ) ) = where ycyOO OO .
cy1 , ycyOi }, yuth = 22yath Oe 1, yuU0 = yuth , yuU1 = .
Oey.
yuth yu
AS R
AS R AS R A1
exp OeAS1R A0 Oe AS2 R A 2 .
yu and yuU2 = th .
yuu Secure two-way relaying with successive interference cancellation and fountain A (Nguyen Thi Ha.
A ISSN: 1693-6930 Considering the source ycI1 , the probability that it correctly receives one packet ycy2 can be given as:
SIC-2TS
yueycISIC-2TS = ycEyc.
aycISIC-2TS Ou yath , yaycISIC-2TS Ou yath ) ycEyc .
aycIIeycI Ou yath ) 1 ,ycy2 1 ,ycyOi 1 IeR,ycy1 2 IeR,ycy2 = ycEyc.
ciycI1ycI Ou yuU0 yuU1 yciycI2 ycI , yciycI2 ycI Ou yuU3 ) ycEyc.
ciRS1 Ou yuU2 ) O = [OyuU yceyciycI2ycI .
Oe yayciycI1ycI .
uU0 yuU1 yc.
) yccycu ] .
Oe yayciRS1 .
uU2 )) .
where yuU3 = yuth 2.
Oey.
yuu We note here that to correctly decode ycy2 , ycI must correctly decode ycy1 first.
Then, substituting .
, after some manipulations, we have:
yueycISIC-2TS 1 ,ycy2 yuIycI2 ycI yuIycI2 ycI yuIycI1 ycI yuU1 yceycuycy (OeyuIycI1ycI .
uU0 yuU2 )) yceycuycy(Oe.
uIycI2ycI yuIycI1 ycI yuU1 )yuU3 ) .
Next, the probability that E intercepts one packet ycy1 in SIC-2TS can be formulated as:
SIC-2TS
SIC-2TS
yuAya,ycy = ycEyc.
aycISIC-2TS Ou yath ) ycEyc.
aycISIC-2TS < yath ) ycEyc.
aycISIC-2TS Ou yath , yaycISIC-2TS < yath ) ycEyc.
aycIIeE,ycy Ou yath ) 1 IeE,ycy1 1 IeE,ycy1 1 IeR,ycy1 2 IeR,ycy2 = ycEyc.
ci a ycI1 ya Ou yuU1 yciycI2ya yuU0 ) ycEyc.
ci a ycI1 ya < yuU1 yciycI2 ya yuU0 ) ycEyc.
ciycI1 ycI Ou yuU0 yuU1 yciycI2 ycI , yciycI2 ycI < yuU3 ) ycEyc.
ciRE Ou yuU2 ) ya1 In .
, ya1 is the probability that ya can correctly decode ycy1 received from ycI1 at the first time slot, and ya2 is the probability that ya can correctly decode ycy1 from ycI at the second time slot.
Similar to .
, we have the following results:
ya1 = yuIycI2 ya yuIycI2 ya yuIycI1 ya yuU1 yceycuycy(OeyuIycI1ya yuU0 ) , ycEyc.
ciRE Ou yuU2 ) = yceycuycy(OeyuIRE yuU2 ) ycEyc.
ciycI1 ycI Ou yuU0 yuU1 yciycI2 ycI , yciycI2ycI < yuU3 ) = yuIycI2 ycI yceycuycy(OeyuIycI1 ycI yuU0 ) yuIycI2 ycI yuIycI1 ycI yuU1 Oe yceycuycy(Oe.
uIycI1 ycI yuU1 yuIycI2ycI )yuU3 )) .
SIC-2TS
Substituting .
, we obtain an exact closed-form expression of yuAya,ycy A E,SIC-2TS AS E exp ( OeAS E A0 ) AS E AS E A1
E AS E exp OeAS E A0 E E AS R exp OeAS R A0 Oe ARE A 2
EE 2
E1 Oe 2
1 Oe exp Oe AS1R A1 AS2 R A3
AS2 E AS1E A1 E E
AS2 R AS1R A1
) ))
A Cth Pr CSSIC-2TS C Cth .
CSSIC-2TS C Cth Pr CRSIC-2TS Ie E,pEI C Cth 1 Ie R,p1 2 Ie R,p2 .
Also, the probability that ya intercepts one packet ycy2 in SIC-2TS can be formulated as:
SIC-2TS
A E,SIC-2TS
= Pr ( CSSIC-2TS Ie E,p C Cth .
CS Ie E,p C Cth ) = Pr ( g
Pr C
SIC-2TS
S1 Ie E,p1 S1E C Cth .
SIC-2TS
S2 Ie E,p2 C A0 A1 gS2 E , gS2 E
) (
) (
CA )
) (
Pr gS1E C A0 A1 gS2 E , gS2 E A A3 Pr gS1R C A0 A1 gS2 R , gS2 R C A3 Pr ( g RE C A2 ) .
In .
, ya3 is the probability that ya can correctly decode ycy2 received from ycI2 at the first time slot, and ya4 is the probability that ya can correctly decode ycy1 and ycyOi from ycI1 and ycI at the first and second time slot, respectively, and then ya can obtain ycy2 by performing the XOR operation between ycy1 and ycyOi .
Using the results in .
, .
, .
to calculate the probabilities in .
, we finally obtain:
TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 420-430
TELKOMNIKA Telecommun Comput El Control
SIC-2TS
yuAya,ycy yuIycI2 ya yceycuycy(OeyuIycI1 ya yuU0 Oe.
uIycI2 ya yuIycI1 ya yuU1 )yuU3 ) yuIycI2 ya yuIycI1 ya yuU1 yuIycI2 ya yuIycI2 ycI yceycuycy(Oe.
uIycI1 ya yuIycI1 ycI )yuU0 Oe.
uIycI2 ycI yuIycI1 ycI yuU1 )yuU3 OeyuIRE yuU2 ) .
uIycI2 ya yuIycI1 ya yuU1 ).
uIycI2 ycI yuIycI1 ycI yuU1 ) .
Oe yceycuycy(Oe.
uIycI2ya yuIycI1ya yuU1 )yuU3 )) .
Considering the DNC-3TS scheme, the probability that one packet ycy1 .
cy2 ) is correctly decoded by the source ycI2 .
cI1 ) can be computed exactly as:
DNC-3TS
yueycIDNC-3TS = ycEyc.
aycIDNC-3TS Ou yath ) ycEyc.
aycIIeycI Ou yath ) = yceycuycy(Oe.
uIycI1 ycI yuIycI2ycI )yuU4 ) , yueycIDNC-3TS
2 ,ycy1 2 ,ycy1 1 ,ycy2 1 IeR,ycy1 DNC-3TS
DNC-3TS
= ycEyc.
aycI1 IeR,ycy2 Ou yath ) ycEyc.
aycIIeycI1,ycy2 Ou yath ) = yceycuycy(Oe.
uIycI2 ycI yuIycI1ycI )yuU4 ) .
23yath Oe1 where yuU4 = yuu Finally, the probability that ya intercepts one packet ycy1 .
cy2 ) in DNC-3TS is computed as:
DNC-3TS
yuAya,ycy = ycEyc.
aycIDNC-3TS Ou yath ) ycEyc.
aycIDNC-3TS < yath ) ycEyc.
aycIDNC-3TS Ou yath ) ycEyc.
aycIDNC-3TS 1 IeE,ycy1 1 IeE,ycy1 1 IeR,ycy1 2 IeR,ycy2 DNC-3TS
DNC-3TS
DNC-3TS
DNC-3TS
yath ) ycEyc.
aycIIeE,ycy1 Ou yath ) ycEyc.
aycI1 IeE,ycy1 < yath ) ycEyc.
aycI1 IeR,ycy1 Ou yath ) ycEyc.
aycI2IeR,ycy2 Ou
DNC-3TS
yath ) ycEyc.
aycIDNC-3TS Ou yath ) ycEyc .
aycIIeE,ycy Ou yath ) = yceycuycy(OeyuIycI1ya yuU4 ) .
2 IeE,ycy2 Oi yceycuycy(OeyuIycI1 ya yuU4 )) yceycuycy(Oe.
uIycI1 ycI yuIRE )yuU4 ) .
Oe yceycuycy(OeyuIycI2 ycI yuU4 ) yceycuycy(Oe.
uIycI2ycI yuIycI2 ya )yuU4 )) .
DNC-3TS
yuAya,ycy = ycEyc.
aycIDNC-3TS Ou yath ) ycEyc.
aycIDNC-3TS < yath ) ycEyc.
aycIDNC-3TS Ou yath ) ycEyc.
aycIDNC-3TS 2 IeE,ycy2 2 IeE,ycy2 2 IeR,ycy2 1 IeR,ycy1 DNC-3TS
DNC-3TS
DNC-3TS
DNC-3TS
yath ) ycEyc.
aycIIeE,ycy2 Ou yath ) ycEyc.
aycI2 IeE,ycy2 < yath ) ycEyc.
aycI1 IeR,ycy1 Ou yath ) ycEyc.
aycI2IeR,ycy2 Ou
DNC-3TS
yath ) ycEyc.
aycIDNC-3TS Ou yath ) ycEyc .
aycIIe E,ycyOi Ou yath ) = yceycuycy(OeyuIycI2 ya yuU4 ) .
Oe 1 IeE,ycy1 yceycuycy(OeyuIycI2 ya yuU4 )) yceycuycy(Oe.
uIycI2 ycI yuIRE )yuU4 ) ( 1 Oe yceycuycy(OeyuIycI1 ycI yuU4 ) yceycuycy(Oe.
uIycI1 ycI yuIycI1ya )yuU4 ) .
OP (SOP) and IP (SIP) performance of SIC-2TS and DNC-3TS At first, ycCycE at the source ycIycn .
cn = 1,.
is defined as the probability that ycIycn cannot gather enough yaycoycnycu packets ycyyc .
c = 1,2, yc O yc.
after the transmission ends, while yaycE at ya .
ith respect to ycuycn ) is the probability that ya can collect at least yaycoycnycu packets ycyycn .
Therefore, ycCycE at ycIycn .
cn = 1,.
in the proposed SIC-2TS scheme can be obtained as:
SIC-2TS
SIC-2TS
yaycoycnycu Oc.
ueycI ) .
OeyueycI ,ycy ,ycy ) OPycISIC-2TS = Ocycu=0 ycn ycn yc ycn yc ya ( ycoycaycu ) ycu a ()) ya ya where ( ycoycaycu ) is the binomial coefficient, i.
, ( ycoycaycu ycoycaycu ) ycu!.
aycoycaycu ()).
ycu ycu Then, yaycE at ya in SIC-2TS, with respect to the data ycuycn , can be expressed as:
SIC-2TS
SIC-2TS
yaycoycaycu Oc.
uAya,ycy ) .
OeyuAya,ycy ycn
SIC-2TS
IPya,ycu ycu=yaycoycnycu ycn ya ( ycoycaycu ) ycu For the DNC-3TS scheme, ycCycE at ycIycn and yaycE with respect to ycuycn can be computed, respectively as:
H min Oe1
H max Oe n E H max E DNC-3TS n OPSDNC-3TS
1 OeA SDNC-3TS
E A Si , p j
i , pj
n=0 E n E
H max
H max Oe n EH E
IPE,DNC-3TS
= Eu E max E A E,DNC-3TS 1 Oe A E,DNC-3TS n = H min E n E Next.
SOP of the ycN scheme is defined as the probability that one of two sources in the ycN scheme is in outage, and SIP of the ycN scheme is defined as the probability that the data ycu1 or ycu2 is intercepted, where ycN OO {SIC-2TS,DNC-3TS}.
Therefore, we can express SOP and SIP in the ycN scheme, respectively as:
ycN ycN SOP ycN = 1 Oe .
Oe OPycIycN1 ).
Oe OPycIycN2 ),SIP ycN = 1 Oe .
Oe IPya,ycu ).
Oe IPya,ycu .
Secure two-way relaying with successive interference cancellation and fountain A (Nguyen Thi Ha.
A ISSN: 1693-6930 Throughput of SIC-2TS and DNC-3TS This subsection evaluates the TP of the SIC-2TS and DNC-3TS schemes at the target rate yath .
Indeed.
TP of SIC-2TS and DNC-3TS can be expressed, respectively as:
TP SIC-2TS =
ya ya .
Oe OPycISIC-2TS ) th .
Oe OPycISIC-2TS ),TP DNC-3TS = th .
Oe OPycIDNC-3TS
Oe OPycIDNC-3TS
RESULTS AND DISCUSSION
This section presents both simulation and theoretical results of TP.
SOP and SIP for SIC-2TS and DNC-3TS.
In the simulations, we place all nodes at the following positions: S1 ( 0,0 ) , ycI2 .
, ya.
cuya , ycya ) = ya.
Oe.
, and ycI.
cuycI , .
, where 0 < ycuycI < 0.
Next, for the illustration only, we fix the values of several system parameters by yu = 3, yua02 = 1, yath = 1, and yaycoycnycu .
Figure 2 shows the TP of the considered schemes as a function of the transmit SNR yuu .
B) with H max = 7, ycuycI = 0.
35, and yu = .
6,0.
As seen from Figure 2.
TP of SIC-2TS scheme is higher than that of DNC-3TS, and TP of both schemes increase when yuu .
B) increases.
Moreover.
TP of SIC-2TS is higher with yu = 0.
Figure 3 compares TP of SIC-2TS and DNC-3TS as yu changes, and with H max = 7, ycuycI = .
15,0.
, yuu = 10.
B), and ya.
Oe.
As observed from Figure 3, the TP performance of DNC-3TS is not affected by the value of yu, while our scheme can obtain the highest throughput at yu = 0.
s ycuycI = 0.
and at yu = 0.
s ycuycI = 0.
It is seen from Figure 3 that if the value of yu is not designed appropriately.
TP of SIC-2TS may be lower than that of DNC-3TS.
From Figures 2 and 3, it is worth noting that the simulation results validate the theoretical ones.
Figure 2.
TP versus yuu .
B) with Hycoycaycu = 7, xR = 0.
35, and yu = .
6,0.
Figure 3.
TP versus yu with yaycoycaycu = 7, ycuR = .
15,0.
, and yuu = 10.
B) Figure 4 illustrates the TP performance as a function of ycuycI when yaycoycaycu yuu = 10.
B), and yu = .
6,0.
7,0.
It can be seen from Figure 4 that as yu = 0.
6, yu = 0.
7, and yu = 0.
SIC-2TS can achieve the highest throughput at ycuycI = 0.
2, ycuycI = 0.
25 and ycuycI = 0.
3, respectively.
In contrast.
TP of DNC-3TS increases with the increase of ycuycI .
Finally, we can see that when the relay is placed near ycI1 .
cuycI is lo.
, the throughput of SIC-2TS is much higher than that of DNC-3TS.
In Figure 5, we compare the SOP and SIP of two considered schemes as yuu changes and with Hycoycaycu = 7, ycuycI = 0.
15, yu = .
6,0.
, and ya.
Oe.
We see that as yuu increases.
SOP of SIC-2TS and DNC-3TS decreases, but SIP of SIC-2TS and DNC-3TS increases.
We also see that the SOP of SIC-2TS is lower than SOP of DNC-3TS at low and medium SNR values.
In addition.
SIP of DNC-3TS is almost higher than SIP of SIC-2TS.
It is also seen that SIP of SIC-2TS with yu = 0.
8 is higher than that with yu = 0.
6, while SOP of SIC-2TS with yu = 0.
8 is only lower than that with yu = 0.
6 as yuu Ou 25 dB.
Figures 6 and 7 present the SOP and SIP performance versus yu and yaycoycaycu , respectively.
From Figure 6, the DNC-3TS scheme obtains better SOP performance, as compared with the SIC-2TS scheme.
However, the SIP performance of SIC-2TS is much better than that of DNC-3TS.
In low yu range, increasing yu can improve TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 420-430 TELKOMNIKA Telecommun Comput El Control SOP performance, whereas it degrades the SIP performance of SIC-2TS scheme.
This is due to the fact that the power allocated for two sources becomes more balanced, enabling effective SIC technique at relay with these yu values, and improving decoding performance for both the relay and eavesdropper.
As a result.
SOP decreases while SIP increases.
Figure 4.
TP versus ycuR with yaycoycaycu = 7, yuu = 10.
B), and yu = .
6,0.
7,0.
Figure 5.
SOP and SIP versus yuu .
B) with yaycoycaycu = 7, ycuycI = 0.
15, and yu = .
6,0.
Figure 6.
SOP and SIP versus yu with yaycoycaycu = 7, ycuR = .
15,0.
, and i = 16.
B) Figure 7.
SOP and SIP versus yaycoycaycu with yu = .
5,0.
, i = 10 .
B), and ycuycI = 0.
Like Hau et al.
Figure 6 also shows that there exist optimal power allocation factors corresponding to the relayAos positions, where the SOP performance of our scheme is best.
However, unlike .
, the optimal .
cuycI , y.
value in SIC-2TS scheme appears in the low yu range rather than at high yu due to differences in the adopted power allocation method.
Figure 7 shows that the SIC-2TS scheme consistently outperforms the DNC-3TS scheme in terms of both the SOP and SIP performance.
Next, when yaycoycaycu increases.
SOP in both schemes decreases, but SIP This is due to the fact that all receivers in two considered schemes have more opportunities to collect a sufficient number of encoded packets for the data recovery.
The results in Figure 8 indicate that the position of the relay significantly impacts both the SOP and SIP performance of the SIC-2TS and DNC-3TS schemes.
When ycuycI is low .
, ycuycI is less than 0.
, the SOP performance of SIC-2TS is better than that of DNC-3TS.
Moreover.
SIC-2TS can achieve better SIP performance than DNC-3TS for all ycuycI values.
Secure two-way relaying with successive interference cancellation and fountain A (Nguyen Thi Ha.
A ISSN: 1693-6930 Figure 9 shows the trade-off between SIP and SOP of the SIC-2TS and DNC-3TS schemes.
At first.
Figure 9 shows that achieving a lower SOP value leads to higher SIP values for both schemes, indicating SOP-SIP trade-off.
We can see that SIC-2TS obtains much better SOP-SIP trade-off performance, i.
, at the same SOP values, the SIP value of SIC-2TS is much lower than that of DNC-3TS.
Moreover, the SOP-SIP trade-off performance of SIC-2TS is better as yaycoycaycu decreases, while that of DNC-3TS is better with higher yaycoycaycu .
Figure 8.
SOP and SIP versus ycuR with yaycoycaycu = 7, i = 12.
B), and yu = .
6,0.
Figure 9.
SIP-SOP trade-off when yu = 0.
6, ycuR = 0.
2, with different yaycoycaycu values CONCLUSION This paper proposed and evaluated the SOP and SIP performance of the secure TWR scheme employing FCs.
SIC, and DNC through theoretical analysis and Monte-Carlo simulations.
The study also examined the impact of key system parameters, including the relayAos position, the power allocation factor, and the maximum number of transmission times, on throughput.
SOP, and SIP.
The obtained results showed that optimal power allocation to the two sources enhances performance, with higher power allocation factors improving SOP.
In addition, when any user is closer to the relay, we can also achieve better SOP Notably, the results demonstrate that the best SOP and SIP performance can be achieved by optimizing the relayAos position, the power allocation factor, and the maximum number of transmission times.
For the SOP-SIP trade-off, the findings revealed an inherent trade-off between SOP and SIP depending on TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 420-430 TELKOMNIKA Telecommun Comput El Control these parameters in both schemes, and SIC-2TS scheme can obtain better SOP-SIP trade-off performance with lower yaycoycaycu values.
Future research will further extend the proposed secure TWR scheme by incorporating EH and HIs effects to evaluate its applicability in emerging 6G and IoT communication FUNDING INFORMATION This work is a part of the research project CS.
B1.
024 funded by Saigon University.
AUTHOR CONTRIBUTIONS STATEMENT
This journal uses the Contributor Roles Taxonomy (CRediT) to recognize individual author contributions, reduce authorship disputes, and facilitate collaboration.
Name of Author Nguyen Thi Hau Tran Trung Duy C : Conceptualization M : Methodology So : Software Va : Validation Fo : Formal analysis ue ue ue ue ue ue ue ue ue ue I : Investigation R : Resources D : Data Curation O : Writing - Original Draft E : Writing - Review & Editing ue ue ue ue ue ue ue ue Vi : Visualization Su : Supervision P : Project administration Fu : Funding acquisition CONFLICT OF INTEREST STATEMENT Authors state no conflict of interest.
DATA AVAILABILITY
Derived data supporting the findings of this study are available from the corresponding author.
REFERENCES