Let Θ(G) denote the Shannon capacity of a graph G. We give an elementary proof equivalence, for any graphs G and H, inequalities Θ(G⊔H)>Θ(G)+Θ(H) Θ(G⊠H)>Θ(G)Θ(H). This was shown independently by Wigderson Zuiddam (2022) using Kadison–Dubois duality Axiom choice.

We prove that, under certain conditions, the capacity of an optical communication channel with in-line, nonlinear filtering (regeneration) elements can be higher than the Shannon capacity for the corresponding linear Gaussian white noise channel.

This paper is concerned with the estimation of state trajectory of linear discrete time dynamic systems subject to parametric uncertainty over the compound erasure channel that uses feedback channel intermittently. For this combined system and channel, using the data processing inequality and a robust version of the Shannon lower bound, a necessary condition on channel capacity for estimation o...

In the previous lectures, we have defined the Shannon Capacity of a graph, Θ(G). This lecture is concerned with the Shannon Capacity of the disjoint union G +H of two graphs G and H. The union of two graphs is, informally, what you get when you just place one graph next to the other. In 1956, Shannon conjectured [1] that Θ(G + H) = Θ(G) + Θ(H). As we will see, this is a very natural conjecture ...

This paper considers the problem of coding over a discrete memoryless channel (DMC) with noiseless feedback. The paper provides a stochastic control view of a variable-length version of the posterior matching scheme which is analyzed via a recently proposed symmetrized divergence, termed Extrinsic Jensen–Shannon (EJS) divergence. In particular, under the variable-length posterior matching schem...

In this article, we investigate the Shannon capacity for L-branch maximal combining ratio (MRC) over generalized multipath fading channel. We derive closed-form expressions of the maximal spectral efficiency over Rayleigh, Rician, Nakagami-m, and Weibull multipath fading channel under flat fading conditions. The results are expressed in terms of Meijer G-functions, which can be evaluated numeri...