On the Impact of a Single Edge on the Network Coding Capacity

In this paper, we study the effect of a single link on the capacity of a network of error-free bit pipes. More precisely, we study the change in network capacity that results when we remove a single link of capacity $\delta$. In a recent result, we proved that if all the sources are directly available to a single super-source node, then removing a link of capacity $\delta$ cannot change the capacity region of the network by more than $\delta$ in each dimension. In this paper, we extend this result to the case of multi-source, multi-sink networks for some special network topologies.Comment: Originally presented at ITA 2011 in San Diego, CA. The arXiv version contains an updated proof of Theorem

On the Impact of a Single Edge on the Network Coding Capacity

In this paper, we study the effect of a single link on the capacity of a network of error-free bit pipes. More precisely, we study the change in network capacity that results when we remove a single link of capacity δ. In a recent result, we proved that if all the sources are directly available to a single super-source node, then removing a link of capacity δ cannot change the capacity region of the network by more than δ in each dimension. In this paper, we extend this result to the case of multi-source, multi-sink networks for some special network topologies

Uplink CoMP under a Constrained Backhaul and Imperfect Channel Knowledge

Coordinated Multi-Point (CoMP) is known to be a key technology for next generation mobile communications systems, as it allows to overcome the burden of inter-cell interference. Especially in the uplink, it is likely that interference exploitation schemes will be used in the near future, as they can be used with legacy terminals and require no or little changes in standardization. Major drawbacks, however, are the extent of additional backhaul infrastructure needed, and the sensitivity to imperfect channel knowledge. This paper jointly addresses both issues in a new framework incorporating a multitude of proposed theoretical uplink CoMP concepts, which are then put into perspective with practical CoMP algorithms. This comprehensive analysis provides new insight into the potential usage of uplink CoMP in next generation wireless communications systems.Comment: Submitted to IEEE Transactions on Wireless Communications in February 201

On Approximating the Sum-Rate for Multiple-Unicasts

We study upper bounds on the sum-rate of multiple-unicasts. We approximate the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts network coding problem with $k$ independent sources. Our approximation algorithm runs in polynomial time and yields an upper bound on the joint source entropy rate, which is within an $O(\log^2 k)$ factor from the GNS cut. It further yields a vector-linear network code that achieves joint source entropy rate within an $O(\log^2 k)$ factor from the GNS cut, but \emph{not} with independent sources: the code induces a correlation pattern among the sources. Our second contribution is establishing a separation result for vector-linear network codes: for any given field $\mathbb{F}$ there exist networks for which the optimum sum-rate supported by vector-linear codes over $\mathbb{F}$ for independent sources can be multiplicatively separated by a factor of $k^{1-\delta}$, for any constant ${\delta>0}$, from the optimum joint entropy rate supported by a code that allows correlation between sources. Finally, we establish a similar separation result for the asymmetric optimum vector-linear sum-rates achieved over two distinct fields $\mathbb{F}_{p}$ and $\mathbb{F}_{q}$ for independent sources, revealing that the choice of field can heavily impact the performance of a linear network code.Comment: 10 pages; Shorter version appeared at ISIT (International Symposium on Information Theory) 2015; some typos correcte