30 problems

Time-average code-length conjecture. The time-average expected codeword lengths should satisfy

Extension conjecture. The theorem remains true for $\gamma>1$.

Robust joint source-channel coding conjecture. If any joint source-channel code exists that achieves the target distortion on average, then there should also exist one that meets t…

An unstable open-loop process is a first-order nonstationary autoregressive process, with the Wiener process as an important special case. Transporting such a process over a noisy…

Let Wyner–Ziv coding denote lossy source coding with decoder side information, and let the second-order term be the term appearing in Theorem. Optimality conjecture. The second-ord…

Let $(S,X)$ follow a non-degenerate joint Gaussian distribution, and consider indirect quadratic lossy source coding, with or without observed source reconstruction. Quadratic Gaus…

Zero-delay coding conjecture. This scheme should achieve the same bitrates predicted by Theorem IV.3(ii) of the source-coding architecture.

Consider the entanglement-assisted source-coding task and the achievability statement in Proposition. Tightness conjecture. The achievability statement in Proposition is also tight…

Let $M$ be the message alphabet, let $\beta\in [0,1)$, and let $\alpha$ denote the uncertainty parameter. Suppose that $\tilde{\Theta}(|M|^\beta)$ messages are sent and that…

Achievability-bound conjecture. $E_\text{r}(R)$ also yields an achievability bound on the error exponent for source coding with quantum side information.

Let $X$ be a source alphabet with $|X|=2$, consisting of symbols $x_1$ and $x_2$, with probabilities $\text{p}(x_1)$ and $\text{p}(x_2)$. Let $\beta_T$, $\beta_0$,…

Let $R^*(D)$ denote the infimum mutual-information rate over generalized causal reproductions $\mathsf{GCR}$ whose long-term distortion is at most $D$, and let $R(D)$ denote the ra…

Infinite-degree-of-freedom projection conjecture. The complexity of $\Lambda_f$, measured by the rate at which the minimax redundancy per sample

Conditional binary AIFV-$m$ redundancy conjecture. Under certain conditions on the size of the source alphabet, the worst-case redundancy of optimal binary AIFV-$m$ codes is

Binary AIFV-$m$ upper-bound conjecture. For every source, the redundancy of an optimal binary AIFV-$m$ code is at most

Binary AIFV-$m$ redundancy conjecture. For every natural number $m$, the worst-case redundancy of optimal binary AIFV-$m$ codes is

Extended AIFV redundancy conjecture. When the alphabet is sufficiently large relative to $m$, the worst-case redundancy of optimal extended binary AIFV codes is

Yamamoto's conjecture. Binary AIFV codes might attain better compression performance when more code trees are allowed to be used.

Let $n_L$ denote the width of the cutset components, and let the distribution redundancy be the redundancy arising from approximating the lines by moment-matching reduced Markov ra…

Consider lossless source coding over networks, and call an edge negligible-capacity when, for every function $f(n)=o(n)$ and all sufficiently large $n$, it can carry $f(n)$ bits no…

Gamma-factor conjecture. The achievability scheme can yield a multiplicative factor as small as

Consider binary correlated source models with joint source-channel coded schemes that exploit the correlation at the receiver. Model-independence conjecture. Joint source-channel c…

Random number generation extracts uniform randomness from a source, while separate lossless source coding compresses correlated sources using random bins; the former is typically a…

Let the source be a single or multivariate Markov source, and consider coding over finite rings in the discussed source-coding setting. Linear coding optimality conjecture. Linear…

Let $\mathcal A$ be the family of channels and let Theorem … can be generalized to “many” stationary ergodic sources. The conjecture proposes extending the theorem beyond the i.i.d…