9 problems

Let $\mathbf{X}\sim\operatorname{Unif}(\mathbb{H}^n)$ be uniformly distributed on the Boolean hypercube, and let $\mathbf{Y}$ be obtained by passing each bit of $\mathbf{X}$ throug…

Kumar–Courtade conjecture. For every such binary $B$,

Let $E_0(R,p)$ denote the random-coding exponent and $E(R,p)$ the reliability function for the binary symmetric channel with crossover probability $p$. The rate $R$ ranges over…

Let $N$ be the block length of a code, and consider generator matrices whose column weights are bounded above by a quantity that grows sublinearly in $N$. Sublinear column-weight c…

Linear-code optimality conjecture. For every block length $n$, a best linear $(n,2)$ code is optimal among all binary $(n,2)$ codes in terms of ML decoding performance.

Near-perfect information-velocity conjecture. As $\delta\to1/2$, the ratio of the learning rates for two and one channel should be arbitrarily close to $1$:

Huleihel et al.'s conjecture. In the regime $p\to 1/2$, the optimal learning rate of the student is

Symmetric test-channel optimality conjecture. Due to symmetry, this choice of $V$ is conjectured to be optimal, up to time sharing.

Let $U$ be the auxiliary random variable in the feedback-based collaborative secrecy encoding problem over binary symmetric channels. The preceding result establishes that $U$ can…