arXiv subjects

Chung Chan

Publications and source records attributed to Chung Chan.

26 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.

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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.

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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.

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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.

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arXiv2015

A Game-theoretic Perspective on Communication for Omniscience

We propose a coalition game model for the problem of communication for omniscience (CO). In this game model, the core contains all achievable rate vectors for CO with sum-rate being equal to a given value. Any rate vector in the core distributes the sum-rate among users in a way that makes all users willing to cooperate in CO. We give the necessary and sufficient condition for the core to be nonempty. Based on this condition, we derive the expression of the minimum sum-rate for CO and show that this expression is consistent with the results in multivariate mutual information (MMI) and coded cooperative data exchange (CCDE). We prove that the coalition game model is convex if the sum-rate is no less than the minimal value. In this case, the core is non-empty and a rate vector in the core that allocates the sum-rate among the users in a fair manner can be found by calculating the Shapley value.

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arXiv2011

On the Degree of Freedom for Multi-Source Multi-Destination Wireless Network with Multi-layer Relays

Degree of freedom (DoF) region provides an approximation of capacity region in high signal-to-noise ratio (SNR) regime, while sum DoF gives the scaling factor. In this correspondence, we analyse the DoF region and sum DoF for unicast layered multi-hop relay wireless networks with arbitrary number of source/destination/relay nodes, arbitrary number of hops and arbitrary number of antennas at each node. The result is valid for quite a few message topologies. We reveal the limitation on capacity of multi-hop network due to the concatenation structure and show the similarity with capacitor network. From the analysis on bound gap and optimality condition, the ultimate capacity of multi-hop network is shown to be strictly inferior to that of single-hop network. Linear scaling law can be established when the number of hops is fixed. At cost of channel state information at transmitters (CSIT) for each component single-hop network, our achievable scheme avoids routing and simplifies scheduling.

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arXiv2008

On Tightness of Mutual Dependence Upperbound for Secret-key Capacity of Multiple Terminals

Csiszar and Narayan[3] defined the notion of secret key capacity for multiple terminals, characterized it as a linear program with Slepian-Wolf constraints of the related source coding problem of communication for omniscience, and upper bounded it by some information divergence expression from the joint to the product distribution of the private observations. This paper proves that the bound is tight for the important case when all users are active, using the polymatroidal structure[6] underlying the source coding problem. When some users are not active, the bound may not be tight. This paper gives a counter-example in which 3 out of the 6 terminals are active.

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arXiv2008

Success Exponent of Wiretapper: A Tradeoff between Secrecy and Reliability

Equivocation rate has been widely used as an information-theoretic measure of security after Shannon[10]. It simplifies problems by removing the effect of atypical behavior from the system. In [9], however, Merhav and Arikan considered the alternative of using guessing exponent to analyze the Shannon's cipher system. Because guessing exponent captures the atypical behavior, the strongest expressible notion of secrecy requires the more stringent condition that the size of the key, instead of its entropy rate, to be equal to the size of the message. The relationship between equivocation and guessing exponent are also investigated in [6][7] but it is unclear which is a better measure, and whether there is a unifying measure of security. Instead of using equivocation rate or guessing exponent, we study the wiretap channel in [2] using the success exponent, defined as the exponent of a wiretapper successfully learn the secret after making an exponential number of guesses to a sequential verifier that gives yes/no answer to each guess. By extending the coding scheme in [2][5] and the converse proof in [4] with the new Overlap Lemma 5.2, we obtain a tradeoff between secrecy and reliability expressed in terms of lower bounds on the error and success exponents of authorized and respectively unauthorized decoding of the transmitted messages. From this, we obtain an inner bound to the region of strongly achievable public, private and guessing rate triples for which the exponents are strictly positive. The closure of this region is equivalent to the closure of the region in Theorem 1 of [2] when we treat equivocation rate as the guessing rate. However, it is unclear if the inner bound is tight.

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