MIMO Gaussian Broadcast Channels with Common, Private and Confidential Messages Ziv Goldfeld Ben Gurion University IEEE Information Theory Workshop September, 2016 Z. Goldfeld Ben Gurion University MIMO Gaussian BCs with Common, Private and Confidential Messages 1
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MIMO Gaussian Broadcast Channels withCommon, Private and Confidential Messages
Ziv Goldfeld
Ben Gurion University
IEEE Information Theory Workshop
September, 2016
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 1
Motivation
Gaussian MIMO channels - model wireless communication.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 2
Motivation
Gaussian MIMO channels - model wireless communication.
Susceptibility of wireless communication to eavesdropping.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 2
Motivation
Gaussian MIMO channels - model wireless communication.
Susceptibility of wireless communication to eavesdropping.
Eavesdroppers are not always a malicious entity:
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 2
Motivation
Gaussian MIMO channels - model wireless communication.
Susceptibility of wireless communication to eavesdropping.
Eavesdroppers are not always a malicious entity:
◮ Legitimate recipient of some messages.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 2
Motivation
Gaussian MIMO channels - model wireless communication.
Susceptibility of wireless communication to eavesdropping.
Eavesdroppers are not always a malicious entity:
◮ Legitimate recipient of some messages.
◮ Eavesdropper of other.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 2
Motivation
Gaussian MIMO channels - model wireless communication.
Susceptibility of wireless communication to eavesdropping.
Eavesdroppers are not always a malicious entity:
◮ Legitimate recipient of some messages.
◮ Eavesdropper of other.
Modern BC scenario - Common, Private and Confidential
messages.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 2
Motivation
Gaussian MIMO channels - model wireless communication.
Susceptibility of wireless communication to eavesdropping.
Eavesdroppers are not always a malicious entity:
◮ Legitimate recipient of some messages.
◮ Eavesdropper of other.
Modern BC scenario - Common, Private and Confidential
messages.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 2
Motivation - Banking Site
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 3
Motivation - Banking Site
Common
Common - Advertisement.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 3
Motivation - Banking Site
CommonPrivate
Common - Advertisement.
Private - On-demand Public info (programs, reports, forecasts).
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 3
Motivation - Banking Site
CommonPrivate
Confidential
Common - Advertisement.
Private - On-demand Public info (programs, reports, forecasts).
Confidential - Online banking (access account, transactions).Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 3
MIMO Gaussian BC - Problem Setup
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 4
MIMO Gaussian BC - Problem Setup
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
User j = 1,2 Observes: Yj = GjX + Zj .
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 4
MIMO Gaussian BC - Problem Setup
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
User j = 1,2 Observes: Yj = GjX + Zj .
Dimensions: X, Y1, Y2, Z1, Z2 ∈ Rt ; G1, G2 ∈ R
t×t.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 4
MIMO Gaussian BC - Problem Setup
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
User j = 1,2 Observes: Yj = GjX + Zj .
Dimensions: X, Y1, Y2, Z1, Z2 ∈ Rt ; G1, G2 ∈ R
t×t.
Noise Processes: i.i.d. samples of Zj ∼ N (0, It), j = 1, 2.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 4
MIMO Gaussian BC - Problem Setup
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
User j = 1,2 Observes: Yj = GjX + Zj .
Dimensions: X, Y1, Y2, Z1, Z2 ∈ Rt ; G1, G2 ∈ R
t×t.
Noise Processes: i.i.d. samples of Zj ∼ N (0, It), j = 1, 2.
Input Covariance Constraint: 1n
∑ni=1 E
[
X(i)X⊤(i)]
� K.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 4
MIMO Gaussian BC - Problem Setup
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
User j = 1,2 Observes: Yj = GjX + Zj .
Dimensions: X, Y1, Y2, Z1, Z2 ∈ Rt ; G1, G2 ∈ R
t×t.
Noise Processes: i.i.d. samples of Zj ∼ N (0, It), j = 1, 2.
Input Covariance Constraint: 1n
∑ni=1 E
[
X(i)X⊤(i)]
� K.
Security Criterion: 1n
I(M1; Yn2 ) −−−→
n→∞0.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 4
MIMO Gaussian BC - Goals
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
Known inner and outer bounds on secrecy-capacity region.
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 5
MIMO Gaussian BC - Goals
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
Known inner and outer bounds on secrecy-capacity region.
Q: Do they match for the MIMO Gaussian case?
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 5
MIMO Gaussian BC - Goals
X
G1
G2
Z1
Z2
Y1
Y2
(M0,M1,M2)
(
M(1)0
,M1
)
(
M(2)0
,M2
)
M1
Known inner and outer bounds on secrecy-capacity region.
Q: Do they match for the MIMO Gaussian case?
Q: Do Gaussian inputs achieve boundary points?
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 5
MIMO Gaussian BC - Some Literature
MIMO Gaussian BCs with Eavesdropping Receivers:
Z. Goldfeld Ben Gurion University
MIMO Gaussian BCs with Common, Private and Confidential Messages 6