# Opportunities and Challenges for Error Control Schemes for Wireless Sensor Networks: A Review
## 4 Review on Energy Consumption and Efficiency Model
### Multi-Hop Network  
As we discussed in Section 2.3, there is re-transmission involved in HARQ. Therefore, the total energy for a system needs to incorporate re-transmission factor \((N_{trx})\). The re-transmission factor depends on Frame Error Rate (FER) of the channel and is equal to \(1/(1-FEC)\). Then, the total energy consumption by HARQ system incorporating re-transmission factor is written as Equation (21) [56]:  
\[E_{total}=N_{trx}.(E_{Dec}^{frame}+E_{trans}^{frame})/frame \tag{21}\]  
where \(E_{Dec}^{frame}\) is the energy consumed to decode a frame and \(E_{trans}^{frame}\) is the energy consumption due to transmission and reception of the frame. In [56], [PERSON] et al. utilise standalone FER performance of convolutional code over Rayleigh fading channel with different memory order system to evaluate \((N_{trx})\). The value of \(E_{Dec}^{frame}\) is computed theoretically using trellis complexity and practically using a TMS320C54x DSP platform. However, the value of \(E_{trans}^{frame}\) calculation is not clearly explained. The normalised energy consumption versus encoder memory order of convolutional code for several SNR ranges from 0 to 10 dB is presented. Finally, the optimal memory order of convolutional code is determined to minimise the energy consumption. The paper evaluates normalised energy consumption due to uncoded codes (with memory order of 2 and 8) and codes with optimised memory order for multi-hop networks (refer to Figure 9). The findings conclude that the convolutional code with optimised memory order according to average SNR at the node reduces overall power consumption compared with uncoded and coded with fixed memory order. The normalised energy consumption calculation in the whole paper does not consider the cost of adaption. In [63; 65], [PERSON] et al. evaluate the energy consumption per information bit for multihop linear sensor model neglecting startup, encoding and decoding energy cost. These papers also calculate optimal number of hops and characteristic distance for multihop linear sensor models. In [63], [PERSON] et al. present energy consumption against bit error probability for Hamming and Golay codes assuming linear array of 1000 m with different numbers of hops i.e., several hop distances. The work in [65] is similar to [63] in a multihop linear sensor model scenario with the addition of BCH codes. The results from these two papers indicate that error correction code is useful when channel condition is poor and energy consumption is at a minimum when the distance between nodes is close to the characteristic distance. In [63; 65], the reliability calculation based on Rayleigh fading channel with FSK modulation and non-coherent detection. The paper lacks clarity on how the expected energy consumption per information bit calculated. The conclusion drawn from these papers are based on neglecting startup, encoding and decoding energy cost. However, these costs can not be neglected in most of the WSN cases. The energy efficiency model considering a re-transmission mechanism is introduced in [71]. This model is based on packet error probability of frame as a reliability factor (including uncoded and BCH coded system). The decoding cost is measured on the number of instructions to execute a BCH decoding algorithm. The calculation is based on Rayleigh fading channel and OQPSK modulation considering coded and uncoded systems for both single hop and multi-hop networks. Table 1 shows a summary of energy consumption and efficiency model for both single hop and multi-hop WSN networks. In practical WSN applications such as home and industry automation, building monitoring and health care monitoring, there exists an SHAS network structure, as some WSN nodes are not energy and computationally constrained. However, there is a lack of research work to develop energy efficiency and a consumption model for an SHAS network incorporating capacity approaching ECC (refer Chapter 2.2) such as LDPC and Turbo codes.