8 problems

Consider broadcasting on regular grids with binary symmetric channels of crossover probability $\delta\in\big(0,\frac{1}{2}\big)$, where every vertex with two inputs uses the same…

No-recovery conjecture. Recovery is impossible for every Boolean function $f$.

Majority recovery conjecture. In the higher-dimensional grid setting, recovery is possible using the Majority function.

Let $\mathcal{Y}^*=\bigcup_{k\in\mathbb{N}\setminus\{0\}}\mathcal{Y}^k$ be the set of nonempty finite strings over $\mathcal{Y}$, let $\{Y_k:k\in\mathbb{N}\}$ be the Markov chain a…

Let $P_{X_k}^{+}$ and $P_{X_k}^{-}$ denote the distributions of the observations at layer $k$ conditioned on the source bit being $1$ and $0$, respectively. Fix…

MIMO generalization conjecture. The results of the paper can be generalized to MIMO broadcasting when

Consider the random DAG model with indegree $d=3$, layer size $L_k=O(\log(k))$, Boolean processing functions at the nodes, noise parameter $\delta$, and reconstruction of the root…

Consider broadcasting from a root through a regular grid in dimension $d$, where each node applies the same processing function and each transmitted bit is independently corrupted…