35 problems

The multi-file setting involves servers storing more than two files, while a two-file-per-server algorithm retrieves files by reducing the problem to instances with two files at ea…

Let $\mathcal{C}$ be the reliable throughput region of the generalized collision channel, and let $\bm f=(f_1,f_2,f_3)$ be a duty factor vector for the three-link example. A point…

For a $K$-user single-input multiple-output (SIMO) multiple access channel with block-fading coherence time $T>1$, consider the sum capacity of the channel. Shamai–Marzetta conject…

Let $t$ be a constant number of channel-output errors, independent of the code length $k$ and the number $n$ of codewords. The explicit construction under consideration has code le…

Consider a slotted multiple-access channel with $n\geq 2$ users. In each slot, let $F[t]$ denote the number of transmitting users, with the value of $F[t]$ reported without error a…

An omniscient adversarial multiple-access channel consists of two encoders transmitting to a common receiver in the presence of an adversary who can observe the transmitted sequenc…

Let $X$ and $Y$ be independent random variables uniformly supported on $A=\{0,1\}^n\subseteq\mathbb Z^n$, with their distributions allowed to differ. For $0\le\alpha\le 1$, let…

Consider a discrete-time Gaussian multiple access channel with transmitters $A$ and $B$, where the destination seeks to recover the computation $w_A\oplus w_B$ rather than the indi…

Alphabet-independence conjecture. The capacity does not depend on $q\ge2$; that is,

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…

Strict sum-rate improvement conjecture. Based on extensive simulations, the proposed scheme is strictly better in terms of sum-rate than the Shaviv–Steinberg scheme whenever

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

Popovski's conjecture. A rate region satisfying

Achievability conjecture. There exists a positive number $P^*(K)$ such that, for every $P\geq P^*(K)$, one can choose real numbers $\beta_2,\ldots,\beta_K$ with $|\beta_k|\geq 1$ s…

Symmetric-capacity conjecture. There exists a threshold such that the symmetric capacity is achievable for the symmetric Gaussian multiple access channel whenever the signal-to-noi…

Zero-outage downlink rate conjecture. The maximal downlink rate that has zero probability of outage is specified by $\Gamma_{B,2}$.

Consider a two-user Gaussian multiple-access channel with power constraints $P_1$ and $P_2$. Let $\mathbf{C}(P_1,P_2)$ denote its capacity region, let…

Optimal test-channel conjecture. The above test channel optimizes the sum rate achievable using nested coset codes.

Consider computation of finite-field addition over a real-addition channel. The cut-set bound is the upper bound on the computation rate obtained by applying the cut-set bound to t…

The channel has two encoders with energy-harvesting states, and achievable regions can be obtained using either Shannon strategies or block Markov coding to convey compressed state…

Let $k$ denote the dimension of the MDS component codes used in the graph-based random-access scheme, with degree distributions chosen according to the coding construction. Larger-…

Extension universality conjecture. For all these extensions, threshold saturation should continue to occur, and spatially coupled codes should achieve near-universal performance.

High-left-degree MAP-boundary conjecture. Increasing the left degree of regular LDPC codes, while keeping the rate constant, should push the MAP boundary towards the boundary of th…

Let $\mathcal{R}_{\textnormal{s-c}}^{\textnormal{ind}}$ denote the inner bound on the capacity region of the double-state multiple-access channel with strictly-causal state informa…

Let $\mathcal{C}_{\textrm{3MAC}}$ denote the capacity region of a ccc-q multiple access channel with three senders, whose inputs $x_1,x_2,x_3$ produce the quantum state…