Bounds on the Communication Rate Needed to Achieve SK Capacity in the Hypergraphical Source Model

Abstract

In the multiterminal source model of Csisz$\text{aˊ}$r and Narayan, the communication complexity, $R_{\text{SK}}$, for secret key (SK) generation is the minimum rate of communication required to achieve SK capacity. An obvious upper bound to $R_{\text{SK}}$ is given by $R_{\text{CO}}$, which is the minimum rate of communication required for \emph{omniscience}. In this paper we derive a better upper bound to $R_{\text{SK}}$ for the hypergraphical source model, which is a special instance of the multiterminal source model. The upper bound is based on the idea of fractional removal of hyperedges. It is further shown that this upper bound can be computed in polynomial time. We conjecture that our upper bound is tight. For the special case of a graphical source model, we also give an explicit lower bound on $R_{\text{SK}}$. This bound, however, is not tight, as demonstrated by a counterexample.

A shorter version has been submitted to IEEE ISIT 2016, Barcelona, Spain

References in corpus (1)

• On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model

Cited by in corpus (1)

• Compressed Secret Key Agreement: Maximizing Multivariate Mutual Information Per Bit