5 problems

Let $X$ and $Y$ be binary random variables with $Y=X\oplus Z$, where under hypothesis $\mathcal{H}=i$, $Z\sim\operatorname{Bernoulli}(p_i)$ independently of $X$, and let the correl…

In distributed hypothesis testing, an encoder observes $X^n$ and communicates at rate $R$ to a detector that also observes $Y^n$. The detector uses the optimal detection rule, and…

The distributed hypothesis-testing problem observes correlated sequences $(X^n,Y^n)$, where an encoder maps $X^n$ to a message at rate $R$, and a detector uses that message togethe…

Exponential tightness conjecture. Except for these two possible improvements, the analysis of this specific scheme is exponentially tight.

Symmetric test-channel optimality conjecture. Due to symmetry, this choice of $V$ is conjectured to be optimal, up to time sharing.