7 problems

Let $X^*$ be the unique capacity-achieving input distribution for the amplitude-constrained AWGN channel with peak-amplitude constraint $|X|\le A$. As $A$ increases, consider the s…

Let $X^*$ be the capacity-achieving input distribution for the amplitude-constrained AWGN channel with peak-amplitude constraint $|X|\le A$, and let $|\operatorname{supp}(X^*)|$ de…

Let $X^*$ be the capacity-achieving input distribution for the amplitude-constrained AWGN channel with peak-amplitude constraint $|X|\le A$, and let $|\operatorname{supp}(X^*)|$ de…

A binary Reed–Muller code $\operatorname{RM}(n,v)$ has length $N=2^n$ and rate $R=\frac{1}{N}\sum_{i=0}^{v}\binom{n}{i}$. Consider the sequence of rate-$1/2$ self-dual Reed–Muller…

Let $D_n(\beta,x)$ be the expression … Here $n$ is the dimension, $A$ is the amplitude constraint, $\beta$ is fixed, and $g_n(x,A)$, $k_n(A)$, and $Q_n(x,A)$ are the quantities app…

Bounded-loss conjecture. For any multi-terminal AWGN information network, an achievable single-letter solution is within a bounded distance from the optimal solution, regardless of…

Finite-support conjecture. An input distribution with cardinality not exceeding the number of quantization bins achieves the channel capacity.