the amplified signals to both sources in the second phase. Although the ANC TWR schemes achieve higher throughput than the DNC TWR ones, the sources in ANC TWR must perform interference cancellation, which is too complex to implement in practice. In [10; 11; 12; 13], joint Successive Interference Cancellation (SIC) and DNC are applied at the common relays and these TWR schemes also use only two phases for the data exchange. In particular, during the first phase, both sources simultaneously transmit their packets to the common relays with different transmit power levels. The common relays then perform SIC to decode the received packets. Finally, the relays apply XOR to the decoded packets and transmit the XOR-ed packet to both sources in the second phase. Recently, many TWR models utilizing new communication techniques have been developed, proposed, and analyzed. The authors in [14; 15] studied the performance of the TWR schemes using radio-frequency energy harvesting (EH), where the transmitters have to harvest energy from the radio signals of the surrounding nodes to transmit data. In [16; 17; 18], the TWR schemes using full-duplex (FD) techniques were proposed, where the source and/or relay nodes were equipped with multi-antennas. Although the FD TWR schemes use only one time slot for the data exchange between two sources, they require high synchronization between all nodes as well as complex interference cancellation implementation. However, the related works in [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18] did not consider fountain coding (FC), which is studied in this paper. Fountain coding (FC) [19; 20] can be efficiently used in wireless communication applications due to its simple implementation and environment condition adaptation ability. In fact, an FC source encodes its data to generate encoded packets (or FC packets), which are continuously sent to a destination. The destination only needs to collect a sufficient number of FC packets to recover the original data from the source. Another advantage of FC is to provide high information security. As proven in [21; 22; 23], if the destination receives a sufficient number of FC packets before the eavesdroppers, the source data will be secure. The authors in [24] proposed a cooperative transmission model that employs FC, non-orthogonal multiple access (NOMA), cooperative jamming technique, and intelligent reflective surfaces (IRS) (or reconfigurable intelligent surface (RIS)) to enhance secrecy performance. IRS or RIS are flat-structured surfaces whose arrays of passive and programmable components used to reflect incoming signals to the intended receivers for enhancing the quality of the received signals [25; 26]. Published works [27] evaluated secrecy performance of IRS-assisted wireless communication networks with presence of an eavesdropper. The authors in [28] proposed a down-link system where a multi-antenna base station uses NOMA to serve two users with the help of RIS. Additionally, both continuous and discrete phase shifting were considered in [28]. Another report [29] also considered the IRS-assisted wireless communication system using NOMA, and evaluated the performance of the proposed system in an interference-limited environment. In [30], the authors considered a multi-IRS down-link scheme utilizing wirelessly EH. Recently, the TWR schemes using RIS have gained much attention of researchers. In [31], the authors evaluated outage probability (OP) and average throughput of IRS-aided TWR schemes, where two sources communicate through the RIS (instead of common relays in the conventional TWR schemes). Reference [32] analyzed performance of IRS-aided TWR networks employing SIC, in terms of OP and ergodic rate. The authors in [33] proposed three power allocation algorithms for RIS-based Decode-and-forward (DF) TWR models to improve the system sum rate. In [34; 35], IRS-aided TWR networks using full-duplex techniques were proposed and analyzed.