Multiple Relay based Reed Muller Network Coded Cooperation for Wireless Communication System

This research article proposes a multiple relay-based Reed–Muller network-coded cooperative (MR-RMNCC) scheme for wireless communication. In the MR-RMNCC scheme, Hadamard transform construction is adopted to build Reed–Muller (RM) codes that effectively achieve network coded-cooperation among multiple sources and multiple relays over slow and fast Rayleigh fading channels. In any network coded-cooperative system, a proper encoding strategy at the relay nodes is vital for achieving an optimum code construction at the destination node. Therefore, the authors have proposed an efficient message bit selection algorithm at relay-2 that optimally selects the message bits. The supremacy of the message bit selection algorithm is demonstrated by Monte–Carlo simulation. Furthermore, the performance bound for average error-probability is also derived for the MR-RMNCC scheme that validates its simulated bit-error-rate performance over a fast Rayleigh fading channel. At the destination node, the MR-RMNCC scheme is jointly decoded by two different decoding strategies, i.e. joint soft maximum likelihood decoding and joint majority logic decoding. Monte–Carlo simulations suggest that the MR-RMNCC scheme not only provides a significant bit-error-rate performance gain over its corresponding coded non-cooperative scheme but also to the existing state-of-the-art RM network-coded cooperative scheme under identical conditions.