Distributed Compute-and-Forward Based Relaying Strategies in Multi-User   Multi-Relay Networks
  In this paper, we propose different practical distributed schemes to solve the rank failure problem in the compute and forward (CMF)-based multi-user multi-relay networks without central coordinator, in which the relays have no prior information about each other. First, a new relaying strategy based on CMF, named incremental compute-and-forward (ICMF), is proposed that performs quite well in terms of the outage probability. We show that the distributed ICMF scheme can even outperform the achievable rate of centralized optimal CMF in strong enough inter relay links, with much less complexity. Then, as the second scheme, amplify-forward and compute (AFC) is introduced in which the equations are recovered in the destination rather than in the relays. Finally, ICMF and AFC schemes are combined to present hybrid compute-amplify and forward (HCAF) relaying scheme, which takes advantages of both ICMF, and AFC and improves the performance of the ICMF considerably. We evaluate the performance of the proposed strategies in terms of the outage probability and compare the results with those of the conventional CMF strategy, the Decode and Forward (DF) strategy, and also the centralized optimal CMF. The results indicate the substantial superiority of the proposed schemes compared with the conventional schemes, specially for high number of users and relays. 
Seyed Mohammad Azimi-Abarghouyi, Mohsen Hejazi, Masoumeh Nasiri-Kenari
cs.IT math.IT