35 problems

Consider the fading channel with coherence coefficient $\alpha=0$, and let the input distribution be subject to the channel's input constraints. A capacity-achieving distribution i…

Let $\delta^*(n,\epsilon)$ denote the highest achievable normalized log-density at block length $n$ and error probability $\epsilon$, and let $\delta^*$ and $V$ denote the Poltyrev…

In a multiple-antenna fading channel without transmitter channel-state information, consider outage capacity rather than ergodic capacity, and allocate the available transmit power…

Minimum-bit-energy conjecture. If

Consider the optimization problem in … . The candidate has coordinates determined by the displayed Lambert-$W$ formulas in the preceding construction and satisfies the constraint ……

Corrected Chernoff-bound conjecture. The function $B_L(z)$ is an upper bound for the lower-tail probability:

Let $\bm{X}$ and $\bm{Y}$ denote the input and received vectors, respectively, and let $\bm{G}$ denote the fading channel. Let $\alpha$ be the coherence coefficient, and write…

Let $\bm{X}=(X_1,\ldots,X_N)$ be the input vector, let $\bm{Y}$ be the received vector in the fading channel, and let $\alpha$ be the coherence coefficient. For an input distributi…

Let $\alpha$ be the coherence coefficient of the first-order Gaussian–Markov fading process, and let the user information rate be the rate of the user message in the fading channel…

Let $C_{\mathrm{no-CSI}}(\delta)$ denote the covert capacity of the non-coherent fast Rayleigh-fading channel, and let an input distribution be represented by its mass points, with…

Consider a non-coherent fast Rayleigh-fading channel with an amplitude-constrained input distribution, where the input distribution is discrete and has one mass point at zero. Two-…

Deterministic approximation conjecture. If $h$ has a Nakagami-$m$ distribution with $m \geq 3$, then the fading channel can be well approximated by a deterministic channel gain wit…

Consider the two-user ergodic fading broadcast channel and the inner bound on its capacity region obtained by Shamai and Tuninetti. Shamai–Tuninetti conjecture. Their inner bound i…

Let $N$ be the polar-code block length, let $A$ be the selected subset of polarized bit-channel indices, let $A^c$ be its complement, and let $B$ be the bit-reversal mapping. The d…

Consider a SIMO block-fading multiple-access channel without channel state information at the receivers (CSIR), and let $T$ denote the relevant block-fading parameter used in the s…

Consider a Rayleigh block-fading multiple-access channel with $\numuser$ single-antenna users, coherence time $\cohtime$, and fixed ratio $\numuser/\cohtime$ in the large-…

MIMO pre-log conjecture. If

Let $n_t$ and $n_r$ denote the numbers of transmit and receive antennas, respectively, let $T$ be the block length, and let $Q$ be the number of symbols assigned to gather informat…

Telatar's conjecture. An optimal covariance matrix is of this form for some $\txantop$, and for sufficiently small error probability $\error$ or sufficiently high signal-to-noise r…

Let $n$ be the block length, let $\epsilon$ be fixed, and let the highest achievable normalized log-density (NLD) be evaluated for an infinite constellation over a fading channel.…

BDUT optimality conjecture. The value $\delta^*$ defined above is the Poltyrev capacity without any transmission constraint. Although the BDUT capacity need not a priori equal the…

Let a linear code be used over a flat fading channel, and let the B-DEC denote the bit-wise decoder and the S-DEC denote the symbol-wise decoder. Asymptotic equivalence conjecture.…

Let $a$ and $b$ be the two signaling symbols subject to the same peak and minimum-power constraints … Let $\sigma_a^2$ and $\sigma_b^2$ denote the received-signal variances when th…

Let $a$ and $b$ be the two signaling symbols, and suppose they satisfy the peak and minimum-power constraints … Let $\mathcal{C}_i^k$ denote the penalty term for the $k$th sensor a…

Let GFS denote the greedy link scheduler introduced for wireless networks with fading channels, and let GMS denote Greedy Maximal Scheduling. The performance of a scheduler is meas…