14 problems

An undirected unicast network consists of an undirected communication network with unicast demands between source–destination pairs. Its achievable rate is the common information r…

Let $K\ge 3$ and let $B=K$, so that every user is connected to every relay. A rate tuple is written as $({R_X},{R_Y},{R_Z},{R_{Z_{\Sigma}}})$, with the components denoting the comm…

Private-message extension conjecture. If the capacity of the $K$-user relay network can be found for any $K$, then the capacity of the $K$-user relay network in which the relay exc…

Simplified exponents-region conjecture. The region $\mathcal{E}^*(R_1,\ldots,R_K,\epsilon_1,\ldots,\epsilon_K)$ is the set of all exponent tuples $(\theta_1,\ldots,\theta_K)$ for w…

Consider a $K$-hop network with $K$ decision centers, expected-rate constraints, and possibly different admissible type-I error probabilities at the decision centers. A multiplexin…

A finite-letter characterization (FLC) has a representation part consisting of functions of the rate variables $R_{ij}$, where $1\leq i,j\leq N$. The authors conjecture that this r…

Very weak edge removal–strong converse equivalence conjecture. An equivalence holds between very weak edge removal and the ordinary strong converse for discrete memoryless networks…

Strong converse conjecture. For a general DMN whose capacity region equals the cut-set region, the strong converse holds: allowing a fixed error probability less than one does not…

Consider lossless source coding over networks, and call an edge negligible-capacity when, for every function $f(n)=o(n)$ and all sufficiently large $n$, it can carry $f(n)$ bits no…

Quasi-concavity conjecture. $\lambda^*$ is a quasi-concave function over $\gamma$.

Let $(f^*,R^*)$ be an optimal solution to the linear program in the paper, and let $B_{\sigma_{SW}}$ denote the Slepian-Wolf rate region, with $\operatorname{Ext}(B_{\sigma_{SW}})$…

A discrete memoryless relay channel (DM-RC) is a relay channel whose channel law is memoryless, and a discrete memoryless multicast network is a multicast network with memoryless c…

A decentralized linear system has state dynamics and local observations of the form … with … A decentralized system is stabilizable when its controllers can stabilize the plant, an…

Consider communication networks with a variable number of network nodes, and compare the role of partial decoding across such networks. Partial-decoding significance conjecture. Th…