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A fundamental challenge in the design of Wireless Sensor Network (WSN) is to enhance the network lifetime. The area around the Sink forms a bottleneck zone due to heavy traffic-flow, which limits the network lifetime in WSN. This work attempts to improve the energy efficiency of the bottleneck zone which leads to overall improvement of the network lifetime by considering a duty cycled WSN. An efficient communication paradigm has been adopted in the bottleneck zone by combining duty cycle and network coding. Studies carried out to estimate the upper bounds of the network lifetime by considering (i) duty cycle, (ii) network coding and (iii) combinations of duty cycle and network coding. The sensor nodes in the bottleneck zone are divided into two groups: simple relay sensors and network coder sensors. The relay nodes simply forward the received data, whereas, the network coder nodes transmit using the proposed network coding based algorithm. Energy efficiency of the bottleneck zone increases because more volume of data will be transmitted to the Sink with the same number of transmissions. This in-turn improves the overall lifetime of the network. Performance metrics, namely, packet delivery ratio and packet latency have also been investigated. A detailed theoretical analysis and simulation results have been provided to show the efficacy of the proposed approach.