15 problems

The capacity-region claim. The capacity region of the $K$-user linear deterministic broadcast channel for this diamond message set is the set of non-negative rate tuples satisfying…

Let $C_{PF}(\mathbf{N},P_T)$ denote the proportional fair capacity of a Gaussian broadcast channel with noise vector $\mathbf{N}$ and total power $P_T$. Let $\preceq$ denote the co…

Consider a two-receiver memoryless broadcast channel with states and receiver message side information (RMSI), together with the corresponding channel without RMSI. Let a transmiss…

Consider a private-message AWGN broadcast channel with $Q>3$ receivers, ordered by noise levels as $N_1\leq N_2\leq\cdots\leq N_Q$. A group leader is the common subgraph obtained f…

Binary-alphabet concave-envelope conjecture. For all $\alpha\geq1$ and all such Markov chains,

Generalized factorization conjecture. For all product channels, all $\lambda\in[0,1]$, all $\alpha\geq1$, and all $p(x_1,x_2)$,

Factorization conjecture. For all product channels, all $\lambda\in[0,1]$, and all $p(x_1,x_2)$,

Let ${\bf\Sigma}_1$ and ${\bf\Sigma}_2$ denote the channel covariance matrices, let $\rho$ be the signal-to-noise ratio, and let $\mathcal R_{\sf weighted}$ be the weighted ergodic…

Let ${\bf\Sigma}_1$ and ${\bf\Sigma}_2$ denote the channel covariance matrices, let $\rho$ be the signal-to-noise ratio, and let $\alpha^{\star}(\rho)$ and $\beta^{\star}(\rho)$ ma…

Convexity conjecture. For the degraded CMLOBCs described above, the capacity region is strictly concave ($\cap$) if and only if

Let a broadcast relay channel with common relay have input alphabets represented by $X,X_1,X_2$ and output alphabets $Y_1,Z_1,Y_2,Z_2$. In the degraded case, the channel satisfies…

We consider the binary skew-symmetric broadcast channel with input $X$ and outputs $Y_1,Y_2$. Let $U,V$ be random variables such that … forms a Markov chain. Nair–Wang information…

Let $k$ be the alphabet size of the channel input, and let $l_s$ be the alphabet size of the code for User 2 in a permutation encoding approach. For an input-symmetric degraded bro…

Let $(U,V)$ be auxiliary random variables and let $X,Y_1,Y_2$ be the input and outputs of the binary skew-symmetric channel with $p=\frac{1}{2}$, such that…

DPC optimality conjecture. If the $K$ decoders are ordered such that