## 2 Related State of the Art Research  
This section introduces the latest research related to this manuscript.  
WBANs extended to multi-hop communication have been studied to increase their lifetime. Many studies on multi-hop WBANs have focused on energy-efficient MAC or routing protocols [23; 24; 25; 26; 27; 28; 29; 30]. For example, previous studies have focused on a cross-layer technique that includes a MAC layer to reduce delay and improve energy efficiency [23; 24; 25]. In [23], a network tree in a distributed manner has been used to guarantee collision free access to the medium and to route data towards the sink. Computer simulation results have shown that the protocol offers low delay and good resilience to mobility. The proposed solution of [24] extended the cooperation at the MAC layer to a cross-layered gradient based routing solution that allows interaction between WBAN and environmental sensors to ensure data delivery from WBANs to a distant gateway. The MAC layer of [25] provided the network layer with local information about the quality of on-body links to enable the WBAN to identify the most reliable links in a distributed manner. Results of [25] have shown the effectiveness of the proposed design which takes advantage of dynamic scheduling and multi-hop relays as warranted by the link conditions. An energy-efficient and low-delay relay selection method for multi-hop WBANs has also been discussed [26; 27]. In [26], a game-theory approach has been proposed to investigate the problem of relay selection and power control with QoS constraints in multiple-access WBANs. Reference [27] considered adaptive power control and routing in multi-hop WBANs, and developed a low overhead energy-efficient routing scheme. The proposed routing protocol has established an energy-efficient end-to-end path as well as adaptively choosing transmission power for sensor nodes. Path loss models have also been considered to evaluate the energy efficiency of multi-hop WBAN topologies in [28]. Ref. [28] has discussed the propagation channel between two half-wavelength dipoles at 2.45 GHz placed near a human body, and then presented an application for cross-layer design to optimize the energy consumption of different topologies. In addition, a security scheme based on PHY characteristics for multi-hop WBANs has been described [29; 30]. The game-theory framework of [29] was proposed, wherein wearable sensor devices interact in the presence of wiretappers and under fading channel conditions to find the most secure multi-hop path to the hub, while adhering to the end-to-end delay requirements. Reference [30] proposed MASK-BAN, a lightweight fast authenticated secret key extraction scheme for intra-WBAN communication. However, those studies did not focus on an error control scheme.  
On the other hand, the analytical expressions for energy efficiency and packet error ratio (PER) have been formulated for two-way relay cooperative communication in [31] which is similar to our work. Then, [31] introduced a hybrid system, which allows switching between the proposed two-way relay, multi-stage one-way relay, and direct link to maximize energy efficiency, and a joint network-channel coding scheme using convolutional and BCH codes. However, [31] did not consider a hybrid automatic repeat request (ARQ), which was applied to our method. In addition, path loss, shadowing, and additive white Gaussian noise (AWGN) have been taken into account, but multi-path or flat fading has not in [31]. On the other hand, this manuscript considers all of them.