Broadcast Approaches to the Diamond Channel

The problem of dual-hop transmission from a source to a destination via two parallel full-duplex relays in block Rayleigh fading environment is investigated. All nodes in the network are assumed to be oblivious to their forward channel gains; however, they have perfect information about their backward channel gains. We also assume a stringent decoding delay constraint of one fading block that makes the definition of ergodic (Shannon) capacity meaningless. The focus of this paper is on simple, efficient, and practical relaying schemes to increase the expected-rate at the destination. For this purpose, various combinations of relaying protocols and the broadcast approach (multi-layer coding) are proposed. For the decode-forward (DF) relaying, the maximum finite-layer expected-rate as well as two upper-bounds on the continuous-layer expected-rate are obtained. The main feature of the proposed DF scheme is that the layers being decoded at both relays are added coherently at the destination although each relay has no information about the number of layers being successfully decoded by the other relay. It is proved that the optimal coding scheme is transmitting uncorrelated signals via the relays. Next, the maximum expected-rate of ON/OFF based amplify-forward (AF) relaying is analytically derived. For further performance improvement, a hybrid decode-amplify-forward (DAF) relaying strategy, adopting the broadcast approach at the source and relays, is proposed and its maximum throughput and maximum finite-layer expected-rate are presented. Moreover, the maximum throughput and maximum expected-rate in the compress-forward (CF) relaying adopting the broadcast approach, using optimal quantizers and Wyner-Ziv compression at the relays, are fully derived. All theoretical results are illustrated by numerical simulations. As it turns out from the results, when the ratio of the relay power to the source power is high, the CF relaying outperforms DAF (and hence outperforms both DF and AF relaying); otherwise, DAF scheme is superior.