In this paper, we present the well-known Reed–Muller (RM) codes for multilevel multirelay vehicular adhoc networks, which can enjoy coded-cooperation among network nodes. At first, we present the code construction principles for a single node/relay scenario and then extend the design principles to the two-level two-relay and, finally, to multilevel multirelay scenarios. The term “level” refers to the fact that different order RM code is used at each relaying node. Plotkin's construction is exploited to utilize RM codes in such coded-cooperative schemes. To achieve an optimum code at the destination node, proper encoding strategy needs to be employed at the relay node. Therefore, we propose a  design criteria  and an  efficient algorithm  for proper bit selection at the relay nodes to achieve the best possible code at the destination. It is observed that the increase in the number of levels as well as relays result in better channel code at the destination, as compared to the lesser number of relays, however, at the cost of increased decoding complexity. The channels considered to analyze the bit error rate (BER) performances of proposed coded-cooperative schemes are fast and slow Rayleigh fading channels. At the destination, soft decision maximum likelihood decoding is employed. Numerical simulations show that the single-relay RM coded-cooperative scheme provides significant BER performance gains over the noncooperative and state-of-the-art distributed turbo coded-cooperative schemes under identical conditions.
['Saqib Ejaz', 'Yang Feng-fan']
Jointly Optimized Reed–Muller Codes for Multilevel Multirelay Coded-Cooperative VANETS