6 problems

MDLVQ optimality conjecture. The algorithm, with an appropriate local adjustment, is also optimal for any values of $K$ and $N$.

Universal MDLVQ index-assignment conjecture. The combined use of the greedy algorithm and local adjustment $\Rsh(a,b)$ solves the problem of optimal MDLVQ index assignment for any…

Finite-index optimality conjecture. For $K>2$, the local adjustment algorithm augmenting the greedy index assignment is conjectured to be optimal for finite $N$.

Let $\Lambda$ be the shaping lattice, let $G(\Lambda)$ denote its normalized second moment, let $R$ denote the transmission rate, and let $C$ denote the capacity of the additive wh…

For each $i\in\{1,\dots,t\}$, consider an $n i$-complex-dimensional translated lattice shaped by a unit-volume complex hypercube, used over the $t\times r$ MIMO channel with a latt…

In the modified two-way relay scheme, let $R_2$ denote the rate of the lattice code used by both users with the same power, and let $\mathrm{SNR}$ denote the corresponding signal-t…