## 1 Introduction
The authors in [19] presented and analyzed relay selection schemes based on the maximization of the SNRs in different hops (first, second, and end-to-end) of a cooperative communication network with multiple EH and DF relays. In [20], the authors proposed an adaptive EH relay power transmission policy for minimizing the outage probability. In [21], an optimal power allocation scheme that jointly considers the optimization of the signal power-splitting ratio and the transmission power allocation was proposed. The authors in [22] studied and analyzed two relay selection schemes in EH cooperative networks with DF technique. They have shown that the lifetime of devices can be significantly improved when using EH. In [23], the authors proposed a joint optimization solution based on geometric programming and binary particle swarm optimization to solve the non-convex problem of joint power-splitting and source-relay selection in an EH relay network with DF. In [24], an optimal power allocation and relay selection strategy to select the optimal cooperative AF relay was proposed. In [25], the authors developed an approximation of the outage probability expression in a two-way relaying system with DF and EH. In a similar context, the authors in [26] proposed an optimal power-splitting and joint source relay selection scheme in a cooperative communication network with EH and DF relays. In this work, we propose coded cooperative schemes with hard information relaying (HIR) and SIR strategies in a multiple EH relay network. The HIR and SIR strategies aim to adequately address the error-propagation problem due to the erroneous decoding at the relays. In the HIR strategy, only relays that correctly decode the received message from the source node are considered in the relay selection process. This may affect the diversity capacity in the case of erroneous decoding at the relays and supports the SIR strategy. In fact, in the SIR strategy, all available relays participate in the relay selection process, even if erroneous decoding occurs in some relays. Thus, SIR can be particularly useful when such relay channels have good channel fading coefficients on the forwarding relay-destination link. In addition, in the HIR strategy, cyclic redundancy check (CRC) bits are needed in the source message to verify the error-free decoding at the relay. This is not the case with the SIR strategy, but additional computational costs arise when using the SIR approach due to the calculation of soft estimated symbols and related modeling. The main contributions of this paper can be summarized as follows:  
* We propose a coded cooperative scheme with HIR strategy and relay selection (CC-HIR-RS). We derive the optimal power-splitting ratio that leads to the capacity maximization of the relaying channel. Exact closed-form expressions for the outage probability performance of the CC-HIR-RS with constant and optimal power-spitting ratios are derived. * We propose a coded cooperative scheme with SIR strategy and relay selection (CC-SIR-RS). First, we prove by means of the normal quantile-quantile (Q-Q) plot technique [27] that the LLRs at the output of the relay soft encoder, under Rayleigh fading channel at the different links, are not Gaussian, which puts the LLR-based GL model [9] in question. Therefore, the LLR-based soft estimated symbols at the output of the relay soft encoder are modeled as output LLRs of a Rayleigh fading channel with additive zero-mean Gaussian noise, which is referred to as a Rayleigh Gaussian LLR (RGL) model. Directives are provided to determine the parameters of the proposed model. In contrast to the SN model in [8] and SS model in [10], the parameters of the proposed RGL model are computed online and forwarded to the destination that is of practical interest. The adequacy of the proposed RGL model is experimentally justified by the outperformance of the coded cooperative scheme with SIR deploying the RGL model compared to that using the GL, SN, and SS models.