66 problems

Let a 2-user multiple-input-single-output broadcast channel have finite-precision channel state information at the transmitter, meaning that the channel estimation error does not i…

Let a MISO broadcast channel be a multiple-input single-output broadcast channel, and suppose that the channel-state information at the transmitter has finite precision. Lapidoth's…

The $3$-user $M_T\times M_R$ rank-deficient MIMO interference channel has transmitters with $M_T$ antennas, receivers with $M_R$ antennas, direct channels of rank $D_0$, and interf…

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 a PLS estimator use a specified number of PLS directions, and let its degrees of freedom be denoted by DoF. PLS degrees-of-freedom conjecture. The degrees of freedom of PLS alw…

Let $\mathcal{R}_q$ be an involutive system of equations of order $q$ in $n$ spacetime dimensions. Let $Z^{(1)}_q$ denote the relevant first-order reduced symbol count, let $m$ be…

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,…

Consider the decentralized MIMO broadcast channel with $(M,N_1,N_2)=(6,3,3)$, where $k$ denotes the number of informed transmit antennas and $\operatorname{DoF}$ denotes the sum de…

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 $C$.

Consider the two-user MIMO broadcast channel with hybrid CSIT settings PN', NP', DN' and ND', where each user's channel state information at the transmitter is respectively perfect…

Full-uplink-DoF conjecture. When $N_c \geq L+1$, it is optimal to have full DoF in the uplink, and consequently the presented cell association and average puDoF are optimal in this…

Atomic-subnetwork extension conjecture. Lemma extends to atomic subnetworks of arbitrarily large sizes.

Algorithm 1 conjecture. Algorithm $1$ can be used to characterize

SLS optimality conjecture. For the $K>3$ user setting, these bounds should be sufficient to identify a regime in which SLS is optimal.

Finiteness conjecture. Only finitely many of these bounds should be non-redundant; determining the precise set of redundant bounds, or proving that only finitely many bounds exist,…

Consider interference networks with $K$ base station–mobile terminal pairs, connectivity parameter $L\geq 1$, and each mobile terminal associated with $N_c$ base stations. Restrict…

General DoF upper-bound conjecture. The total degrees of freedom satisfies

Let $K$ be the number of users in a SISO X-channel, and let $\Lambda(1/3,1/3,1/3)$ denote the specified synergistic alternating CSIT pattern. DoF-scaling conjecture. Under synergis…

Consider the two-user MIMO broadcast channel with a general message set consisting of seven distinct messages, one for each subset of receivers to which the message is intended, un…

Consider a two-user MIMO broadcast channel with private messages, arbitrary antenna configuration, and one of the four Type II hybrid CSIT models, namely the PN, DN, NP, and ND set…

Let the two-user MIMO broadcast channel with common and private messages have arbitrary antenna configuration and one of the four Type II hybrid CSIT models, namely a model in whic…

Full relay-cooperation looseness conjecture. The main reason for this mismatch is that the upper bound is too loose in this range of $M/N$.

Full relay-cooperation looseness conjecture. The upper bound obtained by assuming full cooperation among the relays is loose in general.