arXiv:1503.06333 · IEEE International Symposium on Information Theory (ISIT)

On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT

Zohaib Hassan Awan, Abdellatif Zaidi, Aydin Sezgin

Published Mar 30, 2016• 13 citations

Abstract

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly (P) or with delay (D) to the transmitter. Denoting by S1, S2, and S3the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively, the overall CSIT can then alternate between eight possible states, i.e., (S1, S2, S3) ∈ {P,D}3. We denote by λS1S2S3the fraction of time during which the state S1S2S3occurs. Under these assumptions, we consider the multi-receiver setup and characterize the SDoF region of fixed hybrid states PPD, PDP, and DDP. We then focus our attention on the symmetric case in which λPDD= λDPD. For this case, we establish bounds on the SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF; and shows that, by opposition to encoding separately over different states, joint encoding across the states enables strictly better secure rates.

DOI: 10.1109/isit.2016.7541844

Related papers

On MISO Broadcast Channel With Alternating CSIT and Secrecy Constraints

Zohaib Hassan Awan, Abdellatif Zaidi, Aydin Sezgin

We study the problem of secure transmission over a two-user Gaussian multi-input single-output (MISO) broadcast channel under the assumption that the state of the channel to each receiver is conveyed either perfectly (P) or with delay (D) to the transmitter. Denoting by S1 and S2 the channel state information at the transmitter (CSIT) of user 1 and user 2, respectively, the overall CSIT can then alternate between four possible states, i.e., (S1,S2)∈ {P,D} 2 . We denote by λS1S2 the fraction of time during which the state S1S2 occurs and focus on the symmetric case such that λS1S2 =λS2S1. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we generalize this model to the two-user Gaussian MISO broadcast channel and establish bounds on the SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF; and shows that, by opposition to encoding separately over different states, joint encoding across the states enables strictly better secure rates.

Mar 21, 20150 citations

On Interplay Between Network Topology and Alternating CSIT for Multi-Receiver Wiretap Channel

Zohaib Hassan Awan, Rudolf Mathar

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper under the assumption that links connecting the transmitter to three receivers may have unequal strength statistically. In addition to this, the state of the channel to each receiver is conveyed either perfectly (P) or with delay (D) to the transmitter. Let S1, S2, and S3be the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively. The overall CSIT can then alternate between eight possible states, i.e., (S1, S2, S3) ∈ {P, D}3. We denote by λS1S2S3the fraction of time during which the state S1S2S3occurs; and, focus on a two state topological setting of strong v.s. weak links with symmetric alternating CSIT, λPDD= λDPD. For this setting, we establish an inner bound on the Generalized Secure Degrees of Freedom (GSDoF) region with different topology states. The encoding scheme sheds light on the usage of both resources, i.e., alternating - topology and CSIT; and, shows that as opposed to coding independently over different states, joint encoding across the CSIT and topological states, enables strictly better secure rates.

Asilomar Conference on Signals, Systems and Computers (ACSSC)Oct 1, 20181 citation

Achievable secure degrees of freedom of MISO broadcast channel With alternating CSIT

Zohaib Hassan Awan, Abdellatif Zaidi, Aydin Sezgin

We study the problem of secure transmission over a two-user Gaussian multi-input single-output (MISO) broadcast channel under the assumption that the channel to each receiver is conveyed either perfectly (P) or with delay (D) to the transmitter. Denoting S1and S2to be the channel state information at the transmitter (CSIT) of user 1 and user 2, respectively; the overall CSIT can then alternate between four states, i.e., (S1, S2) ∈ {P,D}2. We denote λS1S2be the fraction of time the state S1S2occurs, and focus on the symmetric case such that λS1S2= λS2S1. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we generalize this model to the two-user Gaussian MISO broadcast channel and establish an inner bound on the SDoF region. This result shows the synergistic SDoF gains of alternating CSIT and illustrates that, as opposed to encoding separately over different states, an improved SDoF region is achievable by joint encoding across these states.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 201413 citations

On the secrecy degrees of freedom of multi-antenna wiretap channels with delayed CSIT

Sheng Yang, Pablo Piantanida, Mari Kobayashi +1 more

The secrecy degrees of freedom (SDoF) of the Gaussian multiple-input and single-output (MISO) wiretap channel is studied under the assumption that delayed channel state information (CSI) is available at the transmitter and each receiver knows its own instantaneous channel. Such scenario is of practical interest since the legitimate receiver may send its channel states to the transmitter which is overheard by the eavesdropper. We first show that a strictly positive SDoF can be guaranteed whenever the transmitter has delayed CSI (either on the legitimate channel or/and the eavesdropper channel). In particular, in the case with delayed CSI on both channels, it is shown that the optimal SDoF is 2=3. We then generalize the result to the two-user Gaussian MISO broadcast channel with confidential messages and characterize the SDoF region when the transmitter has delayed CSI of both receivers. Interestingly, the artificial noise schemes are shown to provide the optimal SDoF region by masking the confidential message to the unintended receiver while aligning the interference at each receiver.

arXiv:1108.1421IEEE International Symposium on Information Theory (ISIT)Jul 1, 201112 citations

On multi-user MISO wiretap channels with delayed CSIT

Ravi Tandon, Pablo Piantanida, Shlomo Shitz Shamai

The multiple-input single-output (MISO) wiretap channel with K legitimate single-antenna receivers, one single-antenna eavesdropper in presence of delayed channel state information at the transmitter (CSIT) is considered. The transmitter is equipped with (K+1) antennas and has independent messages intended for each one of the K legitimate receivers. While for the case of a single receiver wiretap channel, i.e., K = 1, the optimal secure degrees of freedom (SDoF) with delayed CSIT was recently characterized in [1] and shown to be 2/3, the extension to the multi-receiver case (K > 1) is far from straightforward. We present new results and insights for the simplest non-trivial extension of this problem, i.e., for the case of K = 2 receiver MISO wiretap channel with delayed CSIT. The contribution of this paper is two fold: a) an asymptotic achievable scheme is presented for the case of two legitimate receivers which achieves a sum-SDoF of 36/37 and b) a novel converse proof is presented which shows that the sum-SDoF is upper bounded by 16/15.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 201417 citations

Secure MISO Broadcast Channel: An Interplay Between CSIT and Network Topology

Zohaib Hassan Awan, Aydin Sezgin

We study the problem of secure transmission over a Gaussian two-user multi-input single-output (MISO) broadcast channel (BC) under the assumption that links connecting the transmitter to the two receivers may have unequal strength statistically. In addition to this, the state of the channel to each receiver is conveyed in a delayed manner to the transmitter. We focus on a two state topological setting of strong v.s. weak links. Under these assumptions, we first consider the MISO broadcast channel and establish inner and outer bounds on secure generalized degrees of freedom (SGDoF) region with different topology states. The encoding scheme sheds light on the usage of both resources, i.e., topology of the model and delayed channel state information at the transmitter (CSIT); and, allows digitization and multicasting of overheard side information, while transmitting confidential message over the stronger link. Furthermore, for a special class of channels, we show that the established bounds agree and so we characterize the sum SGDoF. Next, we extended this model to the Gaussian MISO two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly (P) or with delay (D) to the transmitter equal fractions of time, while only delayed CSI is available from the eavesdropper to the transmitter. For this case, we first establish an outer bound on the SGDoF region. Next, we develop an achievability scheme that shows that as opposed to coding independently over different states, joint encoding across the alternating CSIT and topological states enables strictly better secure rates.

IEEE Journal on Selected Areas in Information TheoryJan 27, 20216 citations