21 problems

Optimality conjecture. The new obtained modulation formats are optimal for their size and optimization criteria over uncoded single-subcarrier IM/DD channels.

For each integer $q\geqslant 2$, let $H_q$ be the capacity of the $q$-ary ghost-pulse constraint, and note that $H_2=H_{\rm BGP}$ and $H_3=H_{\rm TGP}$. Zero-capacity conjecture. T…

Let $H_{\rm TGP}$ and $H_{\rm BGP}$ denote the capacities of the ternary and binary ghost-pulse constraints, respectively, defined as the asymptotic base-two logarithmic growth rat…

Let $\Phi_4$ denote the kurtosis of 4D symbols, let $\Psi$ denote the variance of the transmitted 4D symbols' energy, and let $\eta$ denote the average nonlinear-interference (NLI)…

A signal constellation has minimum squared Euclidean distance $d^2$ and let $n_d$ denote the number of pairs of constellation points separated by that distance. Alvarado–Guenzi–Agr…

NIS performance-decay conjecture. The performance decay of NIS is caused by this symbol-by-symbol detection strategy: Euclidean-distance detection is optimal only in the linear reg…

Let $W$ be the bandwidth, $\mathcal E$ the average optical intensity, $N_0$ the Gaussian-noise spectral-density parameter, and let $\mathcal C_{\mathrm{BLOIC}}^{\mathrm{AP}}$ denot…

Let $W$ be the bandwidth, $\mathcal E$ the average optical intensity, and $N_0$ the Gaussian-noise spectral-density parameter. Let…

Consider a semiclassical receiver strategy for a received coherent-state codeword that mixes the codeword symbols using an arbitrary circuit of passive optical elements and then ap…

Consider a $K$-mode receiver that applies adaptive passive linear-optical transformations and coherent displacements to a multimode coherent-state input, detecting the resulting ou…

Let a coherent-state codeword be processed by an arbitrary passive linear-optical mixer before being fed into a Dolinar receiver, and allow the control signal to vary arbitrarily o…

Consider a distribution represented in particle form, as in the particle-based GMP-SDBP method, where linear Gaussian message passing is used to account for the pulse-shaper effect…

The single-polarization and dual-polarization systems are compared through achievable information rates (AIRs), with SDBP denoting stochastic digital backpropagation and DBP denoti…

First-quadrant capacity conjecture. The capacity per unit bandwidth of the minimum-phase system should be of the order of the capacity per unit bandwidth of the coherent system wit…

Consider the five quasi-cyclic nonbinary LDPC codes defined over $\operatorname{GF}(2^3)$, with rates $R\in\{0.7,0.75,0.8,0.85,0.9\}$, regular variable-node degree $d_v=3$, and reg…

SD-FEC limit conjecture. The use of the SD-FEC limit paradigm in the reported record results, where a pre-FEC BER threshold obtained for $4$QAM was used for $2048$QAM, is incorrect…

Let an NFT-based communication scheme use nonlinear-frequency-domain multiplexing of users, and let spectral efficiency denote the achievable information rate per unit bandwidth. S…

Let constellation (d) be the constellation from the comparison under discussion, and let $\operatorname{SEP}$ denote its symbol error probability at input powers of…

Consider the continuous-time cross-phase modulation (XPM) channel model of Mitra and Stark. Its channel capacity is lower-bounded by the capacity of a signal-dependent additive whi…

Peak-optical-power conjecture. For any $Omega\thissubset Upsilon$,

Optimality conjecture. All of the proposed constellations are optimal solutions of the optimization problem