Comments on "Finite-SNR Diversity-Multiplexing Tradeoff for Network Coded Cooperative OFDMA Systems"

In the paper "Finite-SNR Diversity-Multiplexing Tradeoff for Network Coded Cooperative OFDMA Systems', the authors adopt a recently proposed subcarrier allocation algorithm aiming at providing optimal frequency diversity to an OFDMA-based network with network-coded cooperation (NCC), where $P$ source nodes transmit independent information to a common destination with the help of $M$ relay nodes, in a frequency-selective channel with $L$ coherence blocks. However, the analysis of the so-called NCC-OFDMA scheme proposed in the aforementioned paper assumes that the subcarrier allocation algorithm is capable of providing full frequency diversity to all the links in the network, which generally does not hold in practice since the allocation is optimal only from the perspective of a single destination. Therefore, in this note we reevaluate the outage probability of the NCC-OFDMA under a more realistic scenario where only the messages addressed to the destination are benefited with the full frequency diversity provided by the subcarrier allocation algorithm, showing that the diversity order is decreased from $L(M+1)$ to $M+L$.