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.
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.
We study the problem of secure transmission over a Gaussian two-user multi-input single-output (MISO) broadcast channel 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 strictly causal 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 wiretap channel and establish bounds on generalized secure degrees of freedom (GSDoF). Next, we extend this model to the two-user MISO broadcast channel and establish inner and outer bounds on GSDoF region with different topology states. The encoding scheme sheds light on the usage of both resources, i.e., topology of the model and strictly causal channel state information at the transmitter (CSIT); and, allows digitization and multi-casting 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 GSDoF.
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.
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.
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.
The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied, in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2∈ {P, D, N}, and the forms P, D, and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between nine possible states corresponding to all possible values of I1I2, with each state occurring for λI1I2fraction of the total duration. We assume that perfect and instantaneous CSI is available at the all receivers. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where λI1I2= λI2I1. The main technical contributions include developing 1) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints, which also highlight the synergistic benefits of inter-state coding for secrecy; 2) new converse proofs via local statistical equivalence and channel enhancement; and 3) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.
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.