26 problems

Properness and feasibility conjecture. A MIMO interference network is IA feasible only if it is proper.

Optimality of symmetric space partitioning. Such an unequal partitioning cannot achieve more AirComp degrees of freedom than equal-dimension partitioning; equivalently, equal-dimen…

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…

Maximum-efficiency conjecture. The maximum efficiency is $d_{max}=1.4998$, achieved when there are $K=3$ users using $N=2{,}001$ subcarriers.

Consider a 3-user $(p,p+1)$ MIMO interference channel with constant channel coefficients, where each transmitter has $p$ antennas and each receiver has $p+1$ antennas. The degrees…

Ramakrishnan et al.'s conjecture. The condition proposed by Das et al. can be reduced to just six constraints.

Ramakrishnan–Das–Maleki–Markopoulou–Jafar–Vishwanath conjecture. Under these assumptions, the algebraic conditions (SC1)–(SC3), namely the three displayed polynomial nonidentity co…

The proposed MIMO opportunistic interference-alignment schemes use weight vectors, with one scheme based on antenna selection and the other based on singular-value decomposition. B…

A complex Gaussian interference channel is a communication network with constant channel coefficients and $K$ users. The one-DoF conjecture. Such a channel has only one degree of f…

All-$K$ lower-bound conjecture. The lower bound

Consider a $K$-user interference channel with limited feedback through a feedback channel. In the three-phase scheme, let $D_1$, $D_2$, and $D_3$ be diagonal coding matrices, so th…

Consider a $K$-user interference channel with limited feedback through a feedback channel. In the multi-phase interactive interference alignment scheme, let $N$ denote the number o…

A linear interference-alignment problem can be represented by multivariate polynomial equations. Call it proper when the number of equations does not exceed the number of involved…

Decomposability conjecture. Decomposability should hold in every over-constrained setting. This conjecture concerns whether independent processing at each antenna, equivalent to sp…

Let a wireless network have a specified number of antennas at each node, perfect global channel knowledge, and generic channels. Spatial scale invariance conjecture. If the number…

Ramakrishnan et al.'s conjecture. The infinite set of conditions for PBNA feasibility can be reduced to just two conditions.

Let $P$ denote the transmit power, $K$ the number of users, and let $\mathcal{R}_{[K]}$ be the achievable rate of the proposed opportunistic interference alignment schemes with $K$…

Consider the three-user MIMO interference channel and its degrees-of-freedom (DoF) outer bound. In the cases where the outer-bound value is fractional, symbol extensions can make t…

Consider a constant $K$-user MIMO interference channel in which each transmitter has $M$ antennas, each receiver has $N$ antennas, and each transmitter sends $D$ independent stream…

Consider a $3K$-user interference channel with $K otinmathbb{Z}^+$? No: let $Kinmathbb{Z}^+$, and partition the transmitter–receiver pairs into groups $G1,G2,ldots,GK$, each contai…

In a MIMO interference network, let active users and secondary users be separated by pre-aligning the interference caused by the secondary transmitters at the active receivers and…

In a single-antenna interference network, let symbol extension mean transmitting over multiple time or frequency dimensions so that interference alignment can exploit additional si…

For a $K$-user MIMO interference channel with $N_t$ transmit antennas and $N_r$ receive antennas, let $d(K,N_t,N_r)$ denote the degrees of freedom achieved by the interference-alig…

A compound MISO broadcast channel has a base station with $M$ transmit antennas and $K$ multicast groups, each containing $J$ single-antenna receivers who request the same independ…

Let $P_p(\lambda_p\bar{c})=\exp(-\lambda_p\bar{c}d_{ii}^2T^{2/\alpha}C(\alpha))$, where $\lambda_p$ is the parent-point intensity, $\bar{c}$ is the mean cluster size, $d_{ii}$ is t…