Distributed decode–forward for relay networks
Sung Hoon Lim, Kwang Taik Kim, and Young-Han Kim
IEEE Transactions on Information Theory, vol. 63, no. 7, pp. 4103–4118, July 2017.
Preliminary results appeared in Proceedings of the IEEE International Symposium on Information Theory, pp. 636–640, Honolulu, Hawaii, July 2014 and Proceedings of the IEEE Information Theory Workshop, pp. 557–561, Hobart, Australia, November 2014.
A new coding scheme for general 
-node relay networks is presented
for unicast, multicast, and broadcast. The proposed distributed
decode–forward scheme combines and generalizes Marton coding for
single-hop broadcast channels and the Cover–El Gamal partial
decode–forward coding scheme for three-node relay channels. The key
idea of the scheme is to precode all the codewords of the entire
network at the source by multicoding over multiple blocks. This
encoding step allows these codewords to carry partial information of
the messages implicitly without complicated rate splitting and
routing. This partial information is then recovered at the relay nodes
and forwarded further. For -node Gaussian unicast, multicast, and
broadcast relay networks, the scheme achieves within 
bits from
the cutset bound, and thus from the capacity (region), regardless of
the network topology, channel gains, or power constraints. Roughly
speaking, distributed decode–forward is dual to noisy network coding,
which generalized compress–forward to unicast, multicast, and multiple
access relay networks.