9 problems

Refined scaling conjecture. As $n$ tends to infinity,

Let $h_n$ denote the normalized conditional entropy in the code ensemble, and let $\tau$ and $\rho$ be the degree sequences appearing in Theorem 1. For each admissible random varia…

Rotor-code conjecture. Under these assumptions, $\phi_\infty(\mathcal{S})$ represents a good quantum LDPC rotor code.

Let $d_c>d_v\geq 3$ be integers satisfying $d_v<\beta_{d_c}d_c$, where $\beta_{d_c}$ is Calkin's threshold. For a positive constant $\lambda$, let $\Gamma_{\lambda}$ be the ensembl…

Let $d_v$ and $d_c$ be integers with $d_c>d_v\geq 3$. A Tanner graph is asymptotically strong if, for every constant $\beta>0$, there is a constant $\alpha>0$ such that its LP deco…

Let $\mathcal{C}$ be an LDPC code, let $\mathcal{D}$ be a decoder diversity set, and let $\mathcal{E}^{[t]}(\Lambda^{(A,B)})$ be the union of the error sets associated with all tra…

Let $(d_v,d_c)$-regular LDPC codes have girth $\Omega\left(\log n\right)$, and transmit them over a binary symmetric channel with cross-over probability $p$. Let $p^*$ be the bit-e…

Let $q$ be an odd prime power, and let $C(1,q)$ and $C(2,q)$ be the codes defined from the incidence structures in the paper. Their dimensions are the integers $\dim C(1,q)$ and…

Stronger pseudocodeword weight conjecture. The resulting LDPC code has