arXiv subjects

Qiaoqiao Zhou

Publications and source records attributed to Qiaoqiao Zhou.

22 records · Page 2Linked to original sources

arXiv2016

A Faster Algorithm for Asymptotic Communication for Omniscience

We propose a modified decomposition algorithm (MDA) to solve the asymptotic communication for omniscience (CO) problem where the communication rates could be real or fractional. By starting with a lower estimation of the minimum sum-rate, the MDA algorithm iteratively updates the estimation by the optimizer of a Dilworth truncation problem until the minimum is reached with a corresponding optimal rate vector. We also propose a fusion method implementation of the coordinate-wise saturation capacity algorithm (CoordSatCapFus) for solving the Dilworth truncation problem, where the minimization is done over a fused user set with a cardinality smaller than the original one. We show that the MDA algorithm is less complex than the existing ones. In addition, we show that the non-asymptotic CO problem, where the communication rates are integral, can be solved by one more call of the CoordSatCapfus algorithm. By choosing a proper linear ordering of the user indices in the MDA algorithm, the optimal rate vector is also the one with the minimum weighted sum-rate.

cs.IT↗

arXiv2016

Incremental and Decremental Secret Key Agreement

We study the rate of change of the multivariate mutual information among a set of random variables when some common randomness is added to or removed from a subset. This is formulated more precisely as two new multiterminal secret key agreement problems which ask how one can increase the secrecy capacity efficiently by adding common randomness to a small subset of users, and how one can simplify the source model by removing redundant common randomness that does not contribute to the secrecy capacity. The combinatorial structure has been clarified along with some meaningful open problems.

cs.IT↗

arXiv2016

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

In the multiterminal source model of Csisz$\text{á}$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.

cs.IT↗

arXiv2016

Fairness in Communication for Omniscience

We consider the problem of how to fairly distribute the minimum sum-rate among the users in communication for omniscience (CO). We formulate a problem of minimizing a weighted quadratic function over a submodular base polyhedron which contains all achievable rate vectors, or transmission strategies, for CO that have the same sum-rate. By solving it, we can determine the rate vector that optimizes the Jain's fairness measure, a more commonly used fairness index than the Shapley value in communications engineering. We show that the optimizer is a lexicographically optimal (lex-optimal) base and can be determined by a decomposition algorithm (DA) that is based on submodular function minimization (SFM) algorithm and completes in strongly polynomial time. We prove that the lex-optimal minimum sum-rate strategy for CO can be determined by finding the lex-optimal base in each user subset in the fundamental partition and the complexity can be reduced accordingly.

cs.IT↗