9 problems

Let a triply-noisy channel have substitution, insertion, and deletion parameters $\varsigma$, $\iota$, and $\delta$, respectively, and let $h_2$ denote the binary entropy function.…

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…

Consider the noisy fragment-recovery channel studied in the paper, with its capacity defined under the model and asymptotic regime above. F minus A conjecture. As in the noiseless…

Noisy-typewriter test-channel conjecture. The optimal test-channel from $\mathsf{Z}$ to $\mathsf{Y}$ should also be a noisy typewriter channel.

Let $N_k(p)$ denote the probability of winning from a heap of size $k$ when each transmitted binary digit is independently erroneous with probability $p$. A move transmits the numb…

Let $N_k(p)$ denote the probability of winning from a heap of size $k$ when each transmitted binary digit is independently erroneous with probability $p$. A move transmits the numb…

Let $P_{Z|X}$ be a strictly positive discrete memoryless channel (DMC), let $\hat{P}_{X_1^n}$ and $\hat{P}_{Y_1^n}$ denote the empirical distributions of the input and output seque…

Let $X$ be a discrete random variable with alphabet $\mathcal{X}=\{1,\ldots,N\}$, whose probabilities are ordered as $p_k=P_X(k)$ with $p_1\geq p_2\geq\cdots\geq p_N$. Let…

Separate inner-bound dominance conjecture. The separate inner bound will always be equal to or better than the joint inner bound when the sources are independent of the main channe…