44 problems

Consider a fully connected constant $K$-user Gaussian interference channel, and let the total number of degrees of freedom (DoF) measure the high-$\mathtt{SNR}$ growth of the maxim…

Consider an $(M_1,N_1),(M_2,N_2)$ two-user MIMO interference channel, with the antenna arrangement and degrees-of-freedom lower bound … where $(x)^+=\max(0,x)$ and $1(\cdot)$ is th…

Let $(N_1,N_2,u,q_1,q_2)$ denote positive channel and power parameters, and let the isotropic condition mean that the maximum in the stated theorem is achieved by isotropic Gaussia…

Let $u\ge 0$, $N_1,N_2\ge 0$, and let $\Sigma_1,A_2\succeq 0$. For random variables $X_i,Z_i$ in $\mathbb{R}^d$, where $d\ge 1$, suppose that … The variables $Z_1,Z_2$ are Gaussian…

DeepIC is a learned coding scheme for interference channels, while Turbo codes use an interleaver, a component that permutes the coded sequence between constituent codes. The paper…

Hexagonal-network cooperation conjecture. For this hexagonal model, a combination of transmitter and receiver cooperation should mitigate most of the interference and essentially e…

In a multilevel topological interference management setting, let QM-TIM$(t_1,t_2,...,t_l)$ denote the quantized channel model with limited quantization bins for interfering links,…

uMAT–MAT gap conjecture. For the same scenario, the DoF gap defined above holds for any number of cells $C$.

uMAT scaling conjecture. Based on the experimental results, the same asymptotic DoF-gap behavior is valid for an arbitrary number of cells $C$.

Geng et al.'s necessity conjecture. The sufficient condition identified in the cited work for TIN optimality is also necessary for TIN optimality in the $K$-user interference chann…

TIN optimality conjecture. Except for a set of channel gain values of measure zero, these IC-type conditions are necessary for TIN to be optimal for the $K$-user interference chann…

A general layered erasure channel has layers indexed by $l\in\{1,\dots,q\}$, and let Theorem $1$ denote the theorem giving an outer bound on its capacity region. The moderate-inter…

Consider the three-user semi-symmetric complex Gaussian interference channel … … … where $P_k=P$ for $k=1,2,3$, and write $\phi(g_1)$ and $\phi(g_2)$ for the phases of $g_1$ and…

Operational-significance conjecture. As in the corresponding point-to-point MIMO results, link adaptation and HARQ will reduce or eliminate the need to use degrees of freedom for d…

Consider a classical-quantum interference channel with two senders and two intended receivers. The quantum Han–Kobayashi achievability conjecture. A quantum version of the Han–Koba…

MLP-bound looseness conjecture. The bound on the multi-letter portion in the converse is too loose.

Let the symmetric LDA-IC-OR have direct-link parameter $n_{11}=n_{22}=n_{\rm S}$ and cross-link parameter $n_{12}=n_{21}=n_{\rm I}=n_{\rm S}\alpha$, where $\alpha$ is non-negative.…

The full outer-bound conjecture. The claim that the per-user information-theoretic degrees of freedom equal $\frac{M_T M_R}{M_T+M_R}$ for arbitrary antenna numbers $M,N$ is correct…

Consider a MIMO interference network and scale the number of antennas at every transmitter and receiver by the same positive factor. Let the information-theoretic degrees of freedo…

Consider a MIMO interference network with generic time variations, and allow linear schemes over arbitrarily long symbol extensions. The information-theoretic degrees of freedom ar…

Let a $K$-user MIMO wireless interference network have $M$ antennas at each transmitter and $N$ antennas at each receiver, with each user seeking $d$ degrees of freedom. A system i…

Consider the $K$-user interference channel and let … is also necessary for TIN to be optimal for the entire generalized degrees-of-freedom (GDoF) region, except for a set of channe…

Consider a $G$-user interference channel, with antenna ratio $\gamma$ and threshold $\gamma_l$ as defined in the source. Let sDoF denote the normalized degrees of freedom, and let…

Let $\gamma$ denote the antenna ratio in the considered MIMO interference channel, and let the decomposition-based approach be the beamforming construction discussed in the source.…

Zero-error time-sharing conjecture. The bounds obtained partially support the conjecture that