7 problems

Cover's conjecture on feedback capacity under doubled power
arXiv@arxiv
Cover's conjecture. The feedback capacity is at most as large as the nonfeedback capacity under twice the power:
Conjecturerefutedfeedback-capacity gaussian-channels information-theory
0
Chen–Berger conjecture on the capacity-achieving information structure for unit-memory channels
arXiv@arxiv
Chen–Berger conjecture. The information structure of the capacity-achieving distribution is
Conjectureopenchannels-with-memory feedback-capacity information-theory
1
Yang–Kavčić–Tatikonda finite-order characterization conjecture for Gaussian feedback capacity
arXiv@arxiv
Yang–Kavčić–Tatikonda's conjecture. $C_{\textit{FB}}$ can be characterized as the solution of a maximization problem whose size depends only on the order of the noise process.
Conjectureopenfeedback-capacity gaussian-channels information-theory
0
Chen–Berger conjecture on the capacity-achieving information structure for unit-memory channels
arXiv@arxiv
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…
Conjectureopenchannels-with-memory feedback-capacity information-theory
0
Information-structure conjecture for randomized maximizing strategies
arXiv@arxiv
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…
Conjectureopenchannels-with-memory feedback-capacity information-theory
0
Conjecture on randomized information structures for directed-information maximization
arXiv@arxiv
Randomized information-structure conjecture. All information structures of deterministic encoders maximizing $I(A^n \rightarrow B^n)$ should translate into analogous information st…
Conjectureopenchannels-with-memory feedback-capacity information-theory
1
Conjectured optimal policy for the three-state trinary zero-error channel
arXiv@arxiv
Conjectured optimal-policy form. The optimal policy of Player 1 is a stochastic matrix satisfying
Conjectureopendynamic-programming feedback-capacity zero-error-information-theory
0

7 problems

Cover's conjecture on feedback capacity under doubled power

Chen–Berger conjecture on the capacity-achieving information structure for unit-memory channels

Yang–Kavčić–Tatikonda finite-order characterization conjecture for Gaussian feedback capacity

Chen–Berger conjecture on the capacity-achieving information structure for unit-memory channels

Information-structure conjecture for randomized maximizing strategies

Conjecture on randomized information structures for directed-information maximization

Conjectured optimal policy for the three-state trinary zero-error channel