The Degraded Gaussian Diamond-Wiretap Channel

In this paper, we present nontrivial upper and lower bounds on the secrecy capacity of the degraded Gaussian diamond-wiretap channel and identify several ranges of channel parameters where these bounds coincide with useful intuitions. Furthermore, we investigate the effect of the presence of an eavesdropper on the capacity. We consider the following two scenarios regarding the availability of randomness: 1) a common randomness is available at the source and the two relays and 2) a randomness is available only at the source and there is no available randomness at the relays. We obtain the upper bound by taking into account the correlation between the two relay signals and the availability of randomness at each encoder. For the lower bound, we propose two types of coding schemes: 1) a decode-and-forward scheme where the relays cooperatively transmit the message and the fictitious message and 2) a partial DF scheme incorporated with multicoding in which each relay sends an independent partial message and the whole or partial fictitious message using dependent codewords.Comment: 26 pages, 6 figures, a short version will appear in Proc. IEEE ISIT 201

LDPC Code Design for the BPSK-constrained Gaussian Wiretap Channel

A coding scheme based on irregular low-density parity-check (LDPC) codes is proposed to send secret messages from a source over the Gaussian wiretap channel to a destination in the presence of a wiretapper, with the restriction that the source can send only binary phase-shift keyed (BPSK) symbols. The secrecy performance of the proposed coding scheme is measured by the secret message rate through the wiretap channel as well as the equivocation rate about the message at the wiretapper. A code search procedure is suggested to obtain irregular LDPC codes that achieve good secrecy performance in such context.Comment: submitted to IEEE GLOBECOM 2011 - Communication Theory Symposiu

Understanding interdependency through complex information sharing

The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work, we propose to analyze these interactions as different modes of information sharing. Towards this end, we introduce a novel axiomatic framework for decomposing the joint entropy, which characterizes the various ways in which random variables can share information. The key contribution of our framework is to distinguish between interdependencies where the information is shared redundantly, and synergistic interdependencies where the sharing structure exists in the whole but not between the parts. We show that our axioms determine unique formulas for all the terms of the proposed decomposition for a number of cases of interest. Moreover, we show how these results can be applied to several network information theory problems, providing a more intuitive understanding of their fundamental limits.Comment: 39 pages, 4 figure

Secure Transmission in Amplify-and-Forward Diamond Networks with a Single Eavesdropper

Unicast communication over a network of $M$-parallel relays in the presence of an eavesdropper is considered. The relay nodes, operating under individual power constraints, amplify and forward the signals received at their inputs. The problem of the maximum secrecy rate achievable with AF relaying is addressed. Previous work on this problem provides iterative algorithms based on semidefinite relaxation. However, those algorithms result in suboptimal performance without any performance and convergence guarantees. We address this problem for three specific network models, with real-valued channel gains. We propose a novel transformation that leads to convex optimization problems. Our analysis leads to (i)a polynomial-time algorithm to compute the optimal secure AF rate for two of the models and (ii) a closed-form expression for the optimal secure rate for the other.Comment: 12pt font, 18 pages, 1 figure, conferenc