42 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…

Let $\chi(\mathcal{N})$ denote the Holevo information of a quantum channel $\mathcal{N}$. Holevo-information additivity conjecture. In the general case, $\chi$ is additive for the…

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…

Csiszár–Narayan conjecture. The mismatch capacity under the maximum-metric decoder for discrete-memoryless channels and product decoding metrics is given by the limiting multi-lett…

Let $N$ be the code block length, and consider low-density generator matrix codes for transmission over binary symmetric channels. A column-weight upper bound is polynomially subli…

Let $\mathcal{N}$ be a quantum channel. Its maximal single-use classical capacity is the capacity achieved with product inputs and a single measurement setting, while…

Let $\Phi$ be a stochastic map, let $\mathcal M=\{E_b\}$ be a measurement, and let $\rho$ be a density matrix. Define … where…

A Gaussian channel has transmitters and receivers connected by channel gains whose structure may resemble that of a quantum pseudo-telepathy game. Quantum pseudo-telepathy enhancem…

Covertness-metric conjecture. For sub-exponential random slot selection, the choice of covertness metric has no impact on the covert-capacity result.

Achievability-refinement conjecture. The relative-entropy bound used in the achievability proof can be refined so as to recover the desired factor of $\sqrt{2}$.

Tightness conjecture. The converse bound is tight and therefore equals the covert capacity.

Capacity-bound conjecture. The upper bound on the covert capacity obtained in this work is the correct covert capacity.

In the relativistic communication model, two twins communicate throughout a journey, and transmission is subject to symmetric constraints for the two observers. Jarett–Cover conjec…

Consider the single-draw noisy shuffling-sampling channel in which each sequence is sampled according to a Bernoulli distribution with parameter $1-q$, and then passed through a di…

Consider a Gaussian MIMO channel with memory under a total (average) power constraint. Its operational capacity is the maximum reliably achievable transmission rate, while its info…

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 $C(d)$ denote the capacity of the binary deletion channel with deletion probability $d\in[0,1]$. Dalai's convexity conjecture. The capacity curve $d\mapsto C(d)$ is convex on t…

Asynchronous-sampling analog-capacity conjecture. The fact that asynchronous sampling captures the entire set of values of the continuous-time noise variance implies that its capac…

Asynchronous-sampling capacity conjecture. The asynchronously-sampled capacity represents the capacity of the analog channel, which is invariant to the sampling mechanism.

Monotonicity conjecture. For all $t\ge 0$, one has

Fixed-parameter AVC capacity conjecture. The capacity is

Let $\mathcal{N}$ be a quantum channel, let $C(\mathcal{N})$ be its classical capacity when measured using a classical encoder and a single measurement setting, and let…

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…