# Energy Efficiency of a Decode-and-Forward Multiple-Relay Network with Rate Adaptive LDPC Codes +
## 1 Introduction  
The Internet of Things (IoT) is a revolutionary communication paradigm, which enables the seamless integration of an excessive amount of devices (e.g., sensors, portable devices, cars, and electronic appliances) with the Internet [1]. Allowing direct interactions between devices or machines with minimal human intervention, IoT reaches various application domains such as smart homes, smart cities, healthcare, and Industry 4.0 [2; 3]. However, such an interconnection between heterogenous devices is the key to paving the road for IoT as a large number of nodes in the IoT networks have very low hardware capabilities with highly limited energy. A cooperative transmission (CT) is known to be an effective solution to thisissue because it provides an signal-to-noise-ratio (SNR) advantage by creating a virtual antenna array using multiple single antenna nodes [4]. This SNR advantage can be used to improve connectivity [5], throughput [6], energy balancing [7], and security [8]. The cooperative transmission with different variants gave birth to a whole new era of research in wireless communications and extensive of work has been done in this area [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35], since their inception in 1971 by [PERSON]. A simple relaying technique has already been in use in cellular networks in the form of repeaters and in satellite communications. When CT is combined with forward error correction (FEC) codes, the communication reliability can be significantly enhanced [10]. In particular, low density parity check (LDPC) codes are considered the best amongst all available FEC codes because of their capacity approaching performance and iterative decoding mechanism [11]. For this reason, there have been numerous studies on LDPC codes for CT-based networks, as in [11; 12; 13]. However, most existing studies on CT adopting LDPC codes have focused on the performance improvement without any consideration of link adaptation techniques. Nonetheless, some researchers have used rate adaptation techniques or more specifically, adaptive coding and modulation (ACM) in cooperative networks, but power allocation was not thoroughly considered. For example, [PERSON] et al. in [14] and [15] discussed the decode-and-forward (DF) multihop systems with ACM, without considering any particular encoding scheme at source and/or relay(s). Moreover, the authors did not consider power allocation optimization at the transmitter. The authors in [16] adapted to different kinds of data rates and different modulation schemes in a non-FEC manner. They did not allocate a fair share of transmit power to each transmitting node. In [17], the authors considered the optimal power allocation technique under the constraint of union bound minimization. Moreover, they only considered a network with source, destination, and a single relay, where no FEC code was applied at the source or at relay. The authors in [18] considered power allocation and minimization of Chernoff bound on bit error rate (BER) performance, but did not consider FEC codes on transmitting nodes. Similarly, in [19], [PERSON] et al. also considered the optimal power allocation for incremental relay selection for hybrid DF and AF relays but they also did not consider channel coding. ACM is studied in [20], where the authors study optimized power allocation for LDPC coded DF relays, however there is no code rate adaptation according to channel state information (CSI). Hence, we delve into a unique scenario, which bridges the gap between the two groups of the researches who either considered the rate adaptation according to channel conditions or considered the optimal power allocation in practical scenarios. To be specific, we investigate a two-hop network with multiple relays where different power allocation techniques are considered under the constraint of energy efficiency.