Partial decode--forward relaying

Partial decode–forward relaying for the Gaussian two-hop relay network

Jing Li and Young-Han Kim

The multicast capacity of the Gaussian two-hop relay network with one source, N relays, and L destinations is studied. It is shown that a careful modification of the partial decode-forward coding scheme, whereby the relays recover and coherently transmit degraded sets of message parts, achieves the cutset upper bound within (1/2)log N bits regardless of the channel gains and power constraints. This scheme improves upon a previous scheme by Chern and Özgür, which is also based on partial decode-forward yet has an unbounded gap from the cutset bound for Lge2 destinations. When restricted to noncoherent transmission among the relays, the proposed partial decode-forward scheme achieves a slightly larger gap of log N bits from the cutset bound. The computation of this relaxed achievable rate involves evaluating mutual information across L(N+1) cuts out of the total L2^N possible cuts, providing a very simple linear-complexity algorithm to approximate the single-source multicast capacity of the Gaussian two-hop relay network.