Flow Decomposition for Multi-User Channels - Part I
Jonathan Ponniah, Liang‐Liang Xie · arXiv (Cornell University) · 2018
A framework based on the idea of flow decomposition is proposed to characterize the decode-forward region for general multi-source, multi-relay, all-cast channels with independent input distributions. The region is difficult to characterize directly when deadlocks occur between two relay nodes, in which both relays benefit by decoding after each other. Rate-vectors in the decode-forward region depend ambiguously on the outcomes of all deadlocks in the channel. The region is characterized indirectly in two phases. The first phase assumes relays can operate non-causally. It is shown that every rate-vector in the decode-forward region corresponds to a set of flow decompositions, which describe the messages decoded at each node with respect to the messages forwarded by all the other nodes. The second phase imposes causal restrictions on the relays. Given an arbitrary set of (possibly non-causal) flow decompositions, necessary and sufficient conditions are derived for the existence of an equivalent set of causal flow decompositions that achieves the same rate-vector region.