5 problems

Let $R_{g,\Lambda}$ denote the matrix associated with the Gaussian $g$ and a lattice $\Lambda$, and let ${x_1}(\Lambda)$ denote the lattice parameter used in the source. Minimal co…

Generalized WAX decomposition validity conjecture. A randomly chosen matrix ${\boldsymbol{H}}$ admits WAX decomposition with probability $1$ for the given ${\boldsymbol{A}}$ if

Let $c_{\mathcal{A}}(s,n)$ denote the relevant coefficient for symbol $s\in\mathcal{S}$ and index $n$. For a fixed $n$, compare the values $c_{\mathcal{A}}(s,n)$ as $s$ ranges over…

Training-based error-probability equivalence conjecture. For the system with $B$ input-output training pairs $(X_B,Y_B)$,

Semi-general asymptotic formula. The outage probability satisfies