6 problems

Let $N$ be the code block length, and consider low-density generator matrix codes for transmission over binary symmetric channels. A column-weight upper bound is polynomially subli…

Let $N$ be the block length of a code, and consider generator matrices whose column weights are bounded above by a quantity that grows sublinearly in $N$. Sublinear column-weight c…

Energy-gap conjecture. The region where

For the $(5,3)$ regular code, let $\underline{I}_{{\mathsf{b}},\mathrm{ext}}^{*(I_{{\mathsf{b}}})}$ and $\overline{I}_{{\mathsf{b}},\mathrm{ext}}^{*(I_{{\mathsf{b}}})}$ denote the…

1RSB exactness conjecture. The one-step-replica-symmetry-breaking formulas for the $N\to+\infty$ limits of the free, internal, and ground-state energies are exact.

In MSE quantization, consider the two properties of the code and $I_{{\mathsf{c}}}$ in density evolution: starting from any $I_{{\mathsf{b}}} \in [0,1]$, density evolution converge…