Distributed Decode-Forward for Relay Networks

A new coding scheme for general N-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 3-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 N-node Gaussian unicast, multicast, and broadcast relay networks, the scheme achieves within 0.5N 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.
Comment: 32 pages, 5 figures, submitted to the IEEE Transactions on Information Theory