6 problems

BEC–BSC twin-Reed–Muller conjecture. The twin-Reed–Muller codes for the BEC and BSC are equivalent; that is, for some $\epsilon=o(1/n)$,

Positive-rate extension conjecture. The conclusion of Corollary 2 should extend from zero-rate code sequences to arbitrary code sequences of positive rate.

MaxEJS blocklength upper-bound conjecture. The expected blocklength satisfies

Let $\mathcal{S}$ be the set of all $n$-dimensional binary sequences, with $S=|\mathcal{S}|=2^n$. Let $H(p)=-p\log p-(1-p)\log(1-p)$ be the binary entropy function, and define … an…

Wolf's conjecture. The constrained BSC capacity satisfies

Let $X^n$ be i.i.d. Bernoulli$(1/2)$, let $Z^n$ be i.i.d. Bernoulli$(\alpha)$ independently of $X^n$, where $0\leq\alpha\leq 1/2$, and let $Y^n=X^n\oplus Z^n$ be the output of the…