24 problems

In an E-FSMC of order $n$, let $\{{b}_{\mathpzc{e}}(t)\}_{t\in\mathbb{Z}}$ be the branch process and let $\{\textbfit{x}^n(t)\}_{t\in\mathbb{Z}}$ be the block-output process, with…

Let $(n)$ be a sequence of polar codes with increasing blocklength $n$, fixed error-probability upper bound $P_e$, rate $\frac{r}{n}$, and channel capacity $C$. The scaling exponen…

Let the degraded binary symmetric broadcast wiretap channel be parameterized by $p$ and $q$, and let the $2$-privacy commitment-capacity upper bound be the quantity given in Eq. ……

Let $\Lambda$ be a formally unimodular lattice, with secrecy function $\Xi_{\Lambda}(\tau)$, and denote its secrecy gain by $\xi_{\Lambda}$. Formally unimodular secrecy-gain conjec…

The accelerated difference-of-convex algorithm (ADCA) is proposed for computing the secrecy capacity and optimal signaling of a Gaussian multiple-input multiple-output wiretap chan…

Let $\kappa_{\Omega}^{(V)}$ denote the auxiliary object used by the polar coding scheme (PCS), and consider the PCS operating to achieve any of the corner points of the relevant ra…

Let $\kappa_{\Omega}^{(V)}$ denote the construction component used in the polar coding scheme, and let strong secrecy mean that the information leakage to the eavesdropper tends to…

The paper compares the secrecy sum-rates of the proposed algorithms with CSSM, a competing method, and observes that CSSM performs better in the reported experiments. Larger-soluti…

Let $(\mathbf T_B,\mathbf T_C)$ be an uncertain wiretap channel, and let $C_0(\mathbf T_B,\mathbf T_C)$ denote its zero-error wiretap capacity. A non-singleton zero-error code is a…

Let $(\mathbf T_B,\mathbf T_C)$ be a general uncertain wiretap channel, and let $C_0(\mathbf T_B,\mathbf T_C)$ denote its zero-error wiretap capacity. Positive-capacity criterion c…

Oggier's conjecture. An optimal transmission for this problem is on the directions where the main channel is stronger than the eavesdropper channel, namely on the positive directio…

Super-activation conjecture. There exist pairs $(\mathfrak W_1,\mathfrak V_1)$ and $(\mathfrak W_2,\mathfrak V_2)$ of finite AVWCs such that

Consider the fast-fading multiple-antenna Gaussian broadcast channel with confidential messages (FM-GBCCM), and let its rate region be the set of achievable rate pairs under a give…

Equivalent-channel conjecture. The secrecy capacity of any general MIMO wiretap channel is given by such an equivalent channel, with

Capacity-based wiretap code conjecture. The result that sequences of random capacity-based wiretap codes can achieve the weak secrecy capacity but cannot achieve the strong secrecy…

The deaf-helper achievability conjecture. The convex hull of the region

Consider a wiretap channel whose main channel and wiretapper's channel are binary memoryless symmetric channels, with the wiretapper's channel degraded with respect to the main cha…

Single-maximum conjecture. The secrecy-capacity curves for finite constellations have a single maximum.

Let $\Lambda$ be an $n$-dimensional unimodular lattice, and let $\Xi_{\Lambda}(y)$ be its secrecy function for $y>0$. The secrecy gain is…

Possible polarization dichotomy. Fix a $0<delta<1$. There exists a partition of $\mathcal{S}_n$ into two sets $\mathcal{S}'_n$ and…

Let $\mathcal{B}_n=emptyset$ in the secrecy polar-coding scheme, so that all cosets used by the scheme are equally likely. The strong-secrecy capacity conjecture. This choice may b…

Two-point convex-hull conjecture. Any point in the convex hull of $\mathscr{C}$ can be expressed as the convex combination of only two points belonging to $\mathscr{C}$. This geome…

Let $U$ be the auxiliary random variable in the feedback-based collaborative secrecy encoding problem over binary symmetric channels. The preceding result establishes that $U$ can…

Complex Gaussian wiretap secrecy-capacity conjecture. For complex channel matrices, the secrecy capacity is