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Register a new userOn Secure Capacity of Multiple Unicast Traffic over Separable Networks
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Added by
Gaurav Kumar Agarwal
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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This paper studies the problem of information theoretic secure communication when a source has private messages to transmit to $m$ destinations, in the presence of a passive adversary who eavesdrops an unknown set of $k$ edges. The information theoretic secure capacity is derived over unit-edge capacity separable networks, for the cases when $k=1$ and $m$ is arbitrary, or $m=3$ and $k$ is arbitrary. This is achieved by first showing that there exists a secure polynomial-time code construction that matches an outer bound over two-layer networks, followed by a deterministic mapping between two-layer and arbitrary separable networks.
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In wireless data networks, communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy systems have become critical for wireless providers and enterprise networks. This paper considers the problem of secret communication over the Gaussian broadcast channel, where a multi-antenna transmitter sends independent confidential messages to two users with perfect secrecy. That is, each user would like to obtain its own message reliably and confidentially. First, a computable Sato-type outer bound on the secrecy capacity region is provided for a multi-antenna broadcast channel with confidential messages. Next, a dirty-paper secure coding scheme and its simplified version are described. For each case, the corresponding achievable rate region is derived under the perfect secrecy requirement. Finally, two numerical examples demonstrate that the Sato-type outer bound is consistent with the boundary of the simplified dirty-paper coding secrecy rate region.
In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matches the algebraic structure of the channel and the joint source distribution fulfills certain conditions, the secrecy computation-capacity equals the computation capacity, which is the supremum of all achievable computation rates without secrecy constraints. Unlike the case of securely transmitting messages, no additional randomness is needed at the encoders nor does the legitimate receiver need any advantage over the eavesdropper. The results therefore show that the problem of securely computing a function over a multiple-access wiretap channel may significantly differ from the one of securely communicating messages.
We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We establish an outer bound on the underlying secure capacity region of the index coding problem, which includes polymatroidal and security constraints, as well as the set of additional decoding constraints for legitimate receivers. We then propose a secure variant of the composite coding scheme, which yields an inner bound on the secure capacity region of the index coding problem. For the achievability of secure composite coding, a secret key with vanishingly small rate may be needed to ensure that each legitimate receiver who wants the same message as the eavesdropper, knows at least two more messages than the eavesdropper. For all securely feasible index coding problems with four or fewer messages, our numerical results establish the secure index coding capacity region.
The problem of multicasting two nested messages is studied over a class of networks known as combination networks. A source multicasts two messages, a common and a private message, to several receivers. A subset of the receivers (called the public receivers) only demand the common message and the rest of the receivers (called the private receivers) demand both the common and the private message. Three encoding schemes are discussed that employ linear superposition coding and their optimality is proved in special cases. The standard linear superposition scheme is shown to be optimal for networks with two public receivers and any number of private receivers. When the number of public receivers increases, this scheme stops being optimal. Two improvements are discussed: one using pre-encoding at the source, and one using a block Markov encoding scheme. The rate-regions that are achieved by the two schemes are characterized in terms of feasibility problems. Both inner-bounds are shown to be the capacity region for networks with three (or fewer) public and any number of private receivers. Although the inner bounds are not comparable in general, it is shown through an example that the region achieved by the block Markov encoding scheme may strictly include the region achieved by the pre-encoding/linear superposition scheme. Optimality results are founded on the general framework of Balister and Bollobas (2012) for sub-modularity of the entropy function. An equivalent graphical representation is introduced and a lemma is proved that might be of independent interest. Motivated by the connections between combination networks and broadcast channels, a new block Markov encoding scheme is proposed for broadcast channels with two nested messages. The rate-region that is obtained includes the previously known rate-regions. It remains open whether this inclusion is strict.
The Langberg-Medard multiple unicast conjecture claims that for any strongly reachable $k$-pair network, there exists a multi-flow with rate $(1,1,dots,1)$. In a previous work, through combining and concatenating the so-called elementary flows, we have constructed a multi-flow with rate at least $(frac{8}{9}, frac{8}{9}, dots, frac{8}{9})$ for any $k$. In this paper, we examine an optimization problem arising from this construction framework. We first show that our previous construction yields a sequence of asymptotically optimal solutions to the aforementioned optimization problem. And furthermore, based on this solution sequence, we propose a perturbation framework, which not only promises a better solution for any $k mod 4 eq 2$ but also solves the optimization problem for the cases $k=3, 4, dots, 10$, accordingly yielding multi-flows with the largest rate to date.
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