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arXiv:1703.01208 · Conference on Information Sciences and Systems

Preserving confidentiality in the Gaussian broadcast channel using compute-and-forward

Parisa Babaheidarian, Somayeh Salimi, Panos Papadimitratos

Published Mar 1, 2017• 2 citations
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Abstract

We study the transmission of confidential messages across a wireless broadcast channel with K > 2 receivers and K helpers. The goal is to transmit all messages reliably to their intended receivers while keeping them confidential from the unintended receivers. We design a codebook based on nested lattice structure, cooperative jamming, lattice alignment, and i.i.d. coding. Moreover, we exploit the asymmetric compute-and-forward decoding strategy to handle finite SNR regimes. Unlike previous alignment schemes, our achievable rates are attainable at any finite SNR value. Also, we show that our scheme achieves the optimal sum secure degrees of freedom of 1 for the K-receiver Gaussian broadcast channel with K confidential messages and K helpers.

DOI
10.1109/ciss.2017.7926077

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We study the transmission of confidential messages across a wireless broadcast channel with K > 2 receivers and K helpers. The goal is to transmit all messages reliably to their intended receivers while keeping them confidential from the unintended receivers. We design a codebook based on nested lattice structure, cooperative jamming, lattice alignment, and i.i.d. coding. Moreover, we exploit the asymmetric compute-and-forward decoding strategy to handle finite SNR regimes. Unlike previous alignment schemes, our achievable rates are attainable at any finite SNR value. Also, we show that our scheme achieves the optimal sum secure degrees of freedom of 1 for the K-receiver Gaussian broadcast channel with K confidential messages and K helpers.
We consider a secure communication scenario through the two-user Gaussian interference channel: each transmitter (user) has a confidential message to send reliably to its intended receiver while keeping it secret from the other receiver. Prior work investigated the performance of two different approaches for this scenario; i.i.d. Gaussian random codes and real alignment of structured codes. While the latter achieves the optimal sum secure degrees of freedom (s.d.o.f.), its extension to finite SNR regimes is challenging. In this paper, we propose a new achievability scheme for the weak and the moderately weak interference regimes, in which the reliability as well as the confidentiality of the transmitted messages are maintained at any finite SNR value. Our scheme uses lattice structure, structured jamming codewords, and lattice alignment in the encoding and the asymmetric compute-and-forward strategy in the decoding. We show that our lower bound on the sum secure rates scales linearly with log(SNR) and hence, it outperforms i.i.d. Gaussian random codes. Furthermore, we show that our achievable result is asymptotically optimal. Finally, we provide a discussion on an extension of our scheme to K > 2 users.
In this work, we consider a K-user Gaussian wiretap multiple-access channel (GW-MAC) in which each transmitter has an independent confidential message for the receiver. There is also an external eavesdropper who intercepts the communications. The goal is to transmit the messages reliably while keeping them confidential from the eavesdropper. To accomplish this goal, two different approaches have been proposed in prior works, namely, i.i.d. Gaussian random coding and real alignment. However, the former approach fails at moderate and high SNR regimes as its achievable result does not grow with SNR. On the other hand, while the latter approach gives a promising result at the infinite SNR regime, its extension to the finite-SNR regime is a challenging task. To fill the gap between the performance of the existing approaches, in this work, we establish a new scheme in which, at the receiver's side, it utilizes an extension of the compute-and-forward decoding strategy and at the transmitters' side it exploits lattice alignment, cooperative jamming, and i.i.d. random codes. For the proposed scheme, we derive a new achievable bound on sum secure rate which scales with log(SNR) and hence it outperforms the i.i.d. Gaussian codes in moderate and high SNR regimes. We evaluate the performance of our scheme, both theoretically and numerically. Furthermore, we show that our sum secure rate achieves the optimal sum secure degrees of freedom in the infinite-SNR regime.
In this paper, we present an achievable security scheme for an interference channel with arbitrary number of users. In this model, each receiver should be able to decode its intended message while it should remain ignorant regarding messages intended for other receivers. Our scheme relies on transmitters to collectively ensure the confidentiality of the transmitted messages using a cooperative jamming technique and lattice alignment. The Asymmetric compute-and-forward framework is used to perform the decoding operation. The proposed scheme is the first asymptotically optimal achievable scheme for this security scenario which scales to arbitrary number of users and works for any finite-valued SNR. Also, our scheme achieves the upper bound sum secure degrees of freedom of 1 without using external helpers and thus the achievable rates lie within constant gap from sum secure capacity.
We study the secure degrees of freedom (s.d.o.f.) for a two-user multiple-input multiple-output (MIMO) Gaussian interference channel with confidential messages, each transmitter–receiver pair of which intends to keep secret from the other pair. Different from existing works on symmetric scenario, in this paper, an asymmetric system is considered, where transmitters haveM1M_1M1​,M2M_2M2​antennas and receivers haveN1N_1N1​,N2N_2N2​antennas, respectively. The channel is assumed to be fast fading and channel matrices are fixed and full rank. We subdivide the problem into several regimes based on the configuration of antennas at each node and present the exact secure degrees of freedom of corresponding regime. To prove a converse, the outer bound is developed by combining information theoretic derivation and the results of fundamental models. We also provide the achievable schemes based on zero forcing, real interference alignment, and cooperative jamming. One part of private signal is sent in the null space, while the other part is sent in a way that it aligns with cooperative jamming signal at unintended receiver, but leaves the secret message intact at intended receiver. As a consequence of the scheme, the objective s.d.o.f. can be achieved and the system ensures that the confidential messages cannot be eavesdropped by unintended receivers.
In this paper, we present an achievable security scheme for an interference channel with arbitrary number of users. In this model, each receiver should be able to decode its intended message while it cannot decode any meaningful information regarding messages intended for other receivers. Our scheme achieves individual secure rates which scale linearly with log(SNR) and achieves sum secure rates which is within constant gap of sum secure capacity. To design the encoders at the transmitters side, we combine nested lattice coding, random i.i.d. codes, and cooperative jamming techniques. Asymmetric compute-and-forward framework is used to perform the decoding operation at the receivers. The novelty of our scheme is that it is the first asymptotically optimal achievable scheme for this security scenario which scales to arbitrary number of users and works for any finite-valued SNR. Also, our scheme achieves the upper bound sum secure degrees of freedom of 111 without using external helpers.
We consider the two-user multiple-input multiple- output (MIMO) interference channel with confidential messages (ICCM). We determine the exact sum secure degrees of freedom (s.d.o.f.) for the symmetric case of M antennas at both transmitters and N antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the IC with no secrecy constraints, and extensions of the secrecy penalty and role of a helper lemmas. We propose a novel achievable scheme for the 2 × 2 ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any M and N by proper vector space operations.