Partial decode–forward relaying for the Gaussian two-hop relay network
Jing Li and Young-Han Kim
IEEE Transactions on Information Theory, vol. 62, no. 12, pp. 7078–7085, December 2016.
Preliminary results appeared in Proceedings of the 52nd Annual Allerton Conference on Communication, Control, and Computing, pp. 785–788, Monticello, Illinois, October 2014.
The multicast capacity of the Gaussian two-hop relay network with one
source, 
relays, and 
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 
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 
destinations. When restricted to noncoherent
transmission among the relays, the proposed partial decode-forward
scheme achieves a slightly larger gap of 
bits from the cutset
bound. The computation of this relaxed achievable rate involves
evaluating mutual information across 
cuts out of the total
possible cuts, providing a very simple linear-complexity
algorithm to approximate the single-source multicast capacity of the
Gaussian two-hop relay network.