Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
An algorithmic framework for wireless information flow
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
A max-flow/min-cut algorithm for a class of wireless networks
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Multicommodity flows and cuts in polymatroidal networks
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Combinatiorial algorithms for wireless information flow
ACM Transactions on Algorithms (TALG)
Bounded-contention coding for wireless networks in the high SNR regime
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr, Diggavi and Tse proposed a linear binary deterministic model that takes into account the shared nature of wireless channels, focusing on the signal interactions rather than the background noise. They generalized the min-cut max-flow theorem for graphs to networks of deterministic channels and proved that the capacity can be achieved using information theoretical tools. They showed that the value of the minimum cut is in this case the minimum rank of all the binary adjacency matrices describing source-destination cuts. However, since there exists an exponential number of cuts, identifying the capacity through exhaustive search becomes infeasible. In this paper, we develop a polynomial time algorithm that discovers the relay encoding strategy to achieve the min-cut value in binary linear deterministic (wireless) networks, for the case of a unicast connection. Our algorithm crucially uses a notion of linear independence between edges to calculate the capacity in polynomial time. Moreover, we can achieve the capacity by using very simple onebit processing at the intermediate nodes, thereby constructively yielding finite length strategies that achieve the unicast capacity of the linear deterministic (wireless) relay network.