8 problems

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

Hassani's conjecture. The lower bound can be tightened up to the BEC's scaling exponent, namely to the numerical value $\mu_{\mathrm{num}}\simeq3.627$.

Let $X^n$ be uniformly distributed over $\\{0,1\\}^n$, let $Y^n$ be obtained by passing $X^n$ through a memoryless binary erasure channel with erasure probability $\epsilon$, and l…

Let $\mu$ denote the scaling exponent of a family of polar codes, meaning that the block length satisfies $n=O\bigl(1/(I(W)-R)^\mu\bigr)$ when the error probability is fixed. For t…

A binary Reed–Muller code $\operatorname{RM}(n,v)$ has length $N=2^n$ and rate $R=\frac{1}{N}\sum_{i=0}^{v}\binom{n}{i}$. Transmission is considered over the binary erasure channel…

Consider codes of positive rate for the binary erasure channel, without assuming that the encoding is linear. Logarithmic update-complexity conjecture. Every such code must have up…

For a binary memoryless symmetric channel, let $\mu$ be the universal scaling parameter governing the rate and block-length trade-off of polar codes under successive cancellation d…

Let transmission take place over the binary erasure channel with erasure probability $\epsilon$, using a code chosen at random from a punctured LDPC ensemble of length $n$ and punc…