8 problems

Let $\mathcal{P}$ be a binary-input memoryless symmetric (BMS) channel with output alphabet $\mathcal{Y}$, and let … be its capacity under the uniform input distribution. For a seq…

Consider the Poisson channel … with power constraint $\tfrac{1}{n}\sum_{t=1}^n x[t] \leq n^\alpha$. This is the Poisson channel with increasing power (PCIP). A normalized rate…

Let $Q$ be a non-uniform distribution and $U$ the uniform distribution on a support of cardinality $2^n$. Let $T$ be the matrix with two rows, $Q$ and $U$, and $2^n$ columns. The q…

Let $W$ be a channel from $[\![1,2]\!]$ to $[\![1,n]\!]$, and let $\mathcal{S}$ be the state space. Suppose … where $S$ denotes the channel state. Causal state-information uselessn…

Let $W$ be a channel and let $\operatorname{dec}(W)$ denote its convex decompositions. For $\lambda\in\operatorname{dec}(W)$, write $\operatorname{C}_{11}(\lambda)$ for the corresp…

A flagged channel randomly selects one channel from a fixed ensemble and reports the selected channel along with the output state. A channel is strongly additive when its use toget…

Cascade-channel capacity conjecture. If $|\mathcal S|<\infty$, so that the channel is finite-state, then the Shannon capacity of the $m$-fold cascade channel converges to…

Super-activation conjecture. There exist pairs $(\mathfrak W_1,\mathfrak V_1)$ and $(\mathfrak W_2,\mathfrak V_2)$ of finite AVWCs such that