Wireless body area networks (WBANs) are composed of sensors that either monitor and transmit vital signals or act as relays that forward the received data to a body node coordinator (BNC). In this paper, we introduce an energy efficient vital signal telemonitoring scheme, which exploits compressed sensing (CS) for low-complexity signal compression/reconstruction and distributed cooperation for reliable data transmission to the BNC. More specifically, we introduce a cooperative compressed sensing (CCS) approach, which increases the energy efficiency of WBANs by exploiting the benefits of random linear network coding (RLNC). We study the energy efficiency of RLNC and compare it with the store-and-forward (FW) protocol. Our mathematical analysis shows that the gain introduced by RLNC increases as the link failure rate increases, especially in practical scenarios with a limited number of relays. Furthermore, we propose a reconstruction algorithm that further enhances the benefits of RLNC by exploiting key characteristics of vital signals. With the aid of electrocardiographic (ECG) and electroencephalographic (EEG) data available in medical databases, extensive simulation results are illustrated, which validate our theoretical findings and show that the proposed recovery algorithm increases the energy efficiency of the body sensor nodes by 40% compared to conventional CS-based reconstruction methods.