19 problems

Maximum-rate conjecture. The maximum achievable rate for square matrix embeddable codes with three or four transmit antennas is $3/4$.

Let $\Lambda$ be a complex signal set, and let $\Delta\Lambda$ denote its difference signal set. Consider an RS-PDSSDC whose variables $x_{1},x_{2},\ldots,x_{N}$ take values from…

Tensor-power conjecture. For every positive integer $m$, the tensor powers

An orthogonal space-time block code (OSTBC) uses orthogonal design to transmit symbols over $n$ antennas, with symbol rate measured in symbols per channel use. Rate conjecture for…

Let ${\mathcal D}$ be an index $n$ ${\mathbb Q}$-central division algebra, let $\Lambda\subset {\mathcal D}$ be an order, and let $\psi_{reg}$ denote its regular representation in…

Consider a non-coherent multiple-input single-output (MISO) system using a non-unitary quasi-orthogonal space-time block code (QOSTBC) with an ABBA construction. For each pair of d…

A space-time block code (STC) used in a multiple-input single-output (MISO) system has a diversity order determined by the ranks of its distance matrices. An orthogonal space-time…

PDF dependence conjecture. The PDF of the channel coefficient only affects the optimal power-loaded vector.

Let $d_1(r)$ be the piecewise linear function connecting the points $(r,[(m-r)(n-2r)]^+)$ where $2r\in\mathbb{Z}$, and let $d_2(r)$ be the piecewise linear function connecting the…

A balanced complex orthogonal design (BCOD) with rate $k/p=1/2$ uses $n=2m$ antennas and has decoding delay $p$, with constructions having $p=2^m$. For $m\equiv 0\pmod 4$, Adams et…

Asymmetric-code suboptimality conjecture. Almost all asymmetric codes with minimum delay are suboptimal from the DMT point of view.

Subsumption conjecture. Most of the existing structured linear space-time codes should be subsumed by the class of DDCs, and hence should be capable of exploiting the low decoding-…

Consider the $2\times1$ MIMO channel, with the EMI-$N$ code and the Alamouti space-time code. Both codes can achieve full diversity, and the Alamouti code has low detection complex…

EMI-$N$ full-diversity rate conjecture. When $N=2$, the bound is achieved: full diversity is still achieved at coding rate $R_c=0.75$. This conjecture concerns whether the upper bo…

Low DoSM non-vanishing determinant conjecture. The proposed scheme with Low DoSM for an SM system with arbitrary $N_t$ has the non-vanishing determinant (NVD) property.

For a positive integer $n$, let $u(n)$ denote the decoding delay of the proposed rate-$frac{1}{2}$ scaled complex orthogonal design for $n$ transmit antennas. **Minimal-delay conj…

Let $n$ be the number of transmit antennas, let $\nu(n)$ denote the decoding delay of the rate-$1/2$ scaled complex orthogonal designs constructed in this paper, and consider rate-…

Traceless discriminant conjecture. For a given signal set, this diversity product is maximum when $2m=n$, equivalently when the discriminant of the code is traceless.

Jiang's conjecture. The optimal LD code for i.i.d. channels with binary inputs is the generalized orthogonal design.