7 problems

Fixed-point threshold conjecture. Assuming that for every $\mathtt{h}\in(\mathtt{h}^{\mathrm{FP}},\log q)$ and $\mathsf{c}\in\\{\mathsf{c}_{\mathtt{h}}\\}$,

Let $w$ be the size of the coupling window, let $E_{\rm f}$ be the true error floor, let $\epsilon>0$, and let $\Delta F_{\rm un}$ denote the relevant free-energy gap in the uncoup…

Potential–MAP threshold conjecture. The potential threshold of nonbinary LDPC codes is identical to the MAP threshold.

Let $Q(x)$ denote the error function associated with the density-evolution analysis, and let the trial entropy be the function obtained by integrating the BP EXIT function…

Negativity conjecture. If $\mathsf{h}^*<\mathsf{h}^{\mathrm{stab}}$, then for every $\mathsf{h}>\mathsf{h}^*$ there exists an $\mathsf{x}\in\mathcal{X}$ such that

Energy-gap conjecture. The region where

Spatial-coupling universality conjecture. The principle of spatial coupling is very general, and threshold saturation should apply to a very broad class of graphical models.