10 problems

For a discrete memoryless arbitrarily varying channel with state constraint $\Lambda$, let the converse region be the rate region established by Theorem. Converse-region conjecture…

Let $\mathcal{C}\subseteq\mathcal{X}^n$ be a $(\lambda,\widehat{P}_{\boldsymbol{x}})$-constant-composition code of size $M$ with $M\geq |\mathcal{X}|^{nR}$ for some constant…

Fixed-parameter AVC capacity conjecture. The capacity is

Let $({N}_t)_{t\in\theta}$ be an arbitrarily varying quantum channel. Its entanglement generating capacity is denoted by $A(({N}_t)_{t\in\theta})$, and the corresponding capacity u…

Let ${\mathfrak I}$ be an arbitrarily varying quantum channel (AVQC), with random message transmission capacity $\overline C_{\mathrm{random}}({\mathfrak I})$ and deterministic mes…

Let ${\mathfrak I}$ be an arbitrarily varying quantum channel (AVQC), with deterministic entanglement transmission capacity $\mathcal A_{\mathrm{det}}({\mathfrak I})$ and random en…

Let ${\mathcal N}\in\mathcal C({\mathcal H},{\mathcal K})$ have a decomposition … where each ${\mathcal N}_s$ is extremal in ${\mathcal C}({\mathcal H},{\mathcal K})$ and $q(s)>0$…

Geometric dirty-paper conjecture. The geometric dirty-paper coding scheme is optimal, in the sense that the encoder cannot exploit the known interference beyond the geometric appro…

Optimal-jammer-direction conjecture. The optimal rate always corresponds to the jammer setting

Adversarial-loss conjecture. The loss of this rate relative to the rate achievable when the jammer's strategy is known is inherent in the adversarial nature of the channel.