7 problems

Chen–Berger conjecture. The information structure of the capacity-achieving distribution is

Let $P$ be a Markov kernel for an ergodic finite-state semi-Markov process, and let the generalised Blahut–Arimoto algorithm optimise the resulting achievable rate. Generalised Bla…

Consider the noisy nanopore channel and a Markov source whose input is transmitted through it. The generalised Blahut–Arimoto algorithm (GBAA) is used to optimise the Markov source…

A noisy nanopore channel is obtained by concatenating an i.i.d. duplication channel with a finite-state semi-Markov channel; finite-state semi-Markov channels are a subclass of cha…

Consider a unit-memory channel with conditional distributions $Q_i(db_i\mid b^{i-1},a^i,x^i)=Q_i(db_i\mid b_{i-1},a_i)$, and let $P_i(da_i\mid a^{i-1},b^{i-1})$ be the channel-inpu…

Let $A^n=(A_0,\ldots,A_n)$ and $B^n=(B_0,\ldots,B_n)$ denote the channel-input and channel-output sequences, and let $I(A^n\rightarrow B^n)$ denote directed information. A determin…

Randomized information-structure conjecture. All information structures of deterministic encoders maximizing $I(A^n \rightarrow B^n)$ should translate into analogous information st…