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Two-way Interference Channels
TexPoint fonts used in EMF.
ITA 2012
Feb. 7
Changho Suh
MIT
Joint work with David Tse & I-Hsiang Wang
Two-way Communication
Network
Two-way Communication
Network
Forward
Backward
Two-way Communication
Network
Communication links are two-way
Two-way Communication
Network
The two-way nature allows interaction
Communication links are two-way
Two-way Communication
Network
Does interaction provide a gain in capacity?
The two-way nature allows interaction
Communication links are two-way
Interaction
Network
Interaction
Network
Prerequisite: Understanding the role of feedback
Interaction
Network
Prerequisite: Understanding the role of feedback
enabled through Feedback
Interaction
Network
Prerequisite: Understanding the role of feedback
enabled through Feedback
Does feedback provide a gain in capacity?
Feedback
Point-to-point
Feedback
Point-to-point
Shannon 56
Feedback
Point-to-point
Feedback cannot increase capacity Shannon 56
Feedback
Point-to-point
Feedback cannot increase capacity Shannon 56
Perfect & cost-free
Feedback
Multiple access
Feedback
Multiple access
Feedback can increase capacity for MACs
(Gaarder-Wolf 75, Cover-Leung 81)
Feedback
Multiple access
Feedback can increase capacity for MACs
(Gaarder-Wolf 75, Cover-Leung 81)
However, gain for AWGN is bounded (Ozarow 84)
Feedback under Interference
Feedback under Interference
Feedback can provide unbounded gain
(Kramer ‘02, Suh-Tse ‘09)
Feedback under Interference
Perfect & cost-free
Feedback can provide unbounded gain
(Kramer ‘02, Suh-Tse ‘09)
Feedback under Interference
Perfect & cost-free
Feedback can provide unbounded gain
(Kramer ‘02, Suh-Tse ‘09)
What if we count feedback cost?
Net Feedback Gain?
Net Feedback Gain?
Bit Pipe
Vahid-Suh-Avestimehr 11:
Net Feedback Gain?
Bit Pipe
One bit of feedback provides one bit of a capacity increase
Vahid-Suh-Avestimehr 11:
Net Feedback Gain?
Bit Pipe
One bit of feedback provides one bit of a capacity increase
Vahid-Suh-Avestimehr 11:
No net feedback gain
Two-way IC: Feedback Over-the-IC
Two-way IC: Feedback Over-the-IC
Two-way IC: Feedback Over-the-IC
Not necessarily same
Two-way IC: Feedback Over-the-IC
Two-way IC: Feedback Over-the-IC
Two-way IC: Feedback Over-the-IC
Forward
time
time
Feedback
Different symbol rates
Two-way IC: Feedback Over-the-IC
Forward
time
time
Feedback
Two-way IC: Feedback Over-the-IC
Forward
time
time
Feedback
Two-way IC: Feedback Over-the-IC
Forward
time
time
(Avestimehr-Diggavi-Tse model ’07)
Feedback
Two-way IC: Feedback Over-the-IC
Forward
time
time
(Avestimehr-Diggavi-Tse model ’07)
Feedback
Two-way IC: Feedback Over-the-IC
Forward
time
time
(Avestimehr-Diggavi-Tse model ’07)
Feedback
Two-way IC: Feedback Over-the-IC
Forward
time
time
(Avestimehr-Diggavi-Tse model ’07)
Feedback
Two-way IC: Feedback Over-the-IC
Forward
time
time
(Avestimehr-Diggavi-Tse model ’07)
Feedback
Sum Capacity
Theorem:
Sum Capacity
Theorem:
Sum Capacity
Theorem:
Sum Capacity
Theorem:
Net Feedback Gain
Net Feedback Gain
Two ways of using backward IC
Net Feedback Gain
Two ways of using backward IC
Send independent backward messages (1)
Net Feedback Gain
Two ways of using backward IC
Send independent backward messages
(2) Send feedback signals for aiding forward-
message tx
(1)
Net Feedback Gain
Two ways of using backward IC
Send independent backward messages
(2) Send feedback signals for aiding forward-
message tx
(1)
Net Feedback Gain
Two ways of using backward IC
Send independent backward messages
(2) Send feedback signals for aiding forward-
message tx
capacity gain
(1)
Net Feedback Gain
Two ways of using backward IC
Send independent backward messages
(2) Send feedback signals for aiding forward-
message tx
capacity gain
(1)
Net Feedback Gain
Two ways of using backward IC
Send independent backward messages
(2) Send feedback signals for aiding forward-
message tx
capacity gain
(1)
Net Feedback Gain
Two ways of using backward IC
Send independent backward messages
(2) Send feedback signals for aiding forward-
message tx
Capacity
Gain
(1) First purpose
capacity gain
(1)
Net Feedback Gain
Two ways of using backward IC
Send independent backward messages
(2) Send feedback signals for aiding forward-
message tx
Capacity
Gain
(1) First purpose
capacity gain
(1)
Net Feedback Gain
Two ways of using backward IC
(2) Send feedback signals for aiding forward-
message tx
Capacity
Gain
(1) First purpose
(2) Feedback purpose
capacity gain
Send independent backward messages (1)
Net Feedback Gain
Two ways of using backward IC
(2) Send feedback signals for aiding forward-
message tx
Capacity
Gain
(1) First purpose
(2) Feedback purpose
$
capacity gain
(cost)
Send independent backward messages (1)
Net Feedback Gain
Two ways of using backward IC
(2) Send feedback signals for aiding forward-
message tx
Capacity
Gain
(1) First purpose
(2) Feedback purpose
$
0.5 bits
capacity gain
(cost)
Send independent backward messages (1)
Net Feedback Gain
Two ways of using backward IC
(2) Send feedback signals for aiding forward-
message tx
Capacity
Gain
(1) First purpose
(2) Feedback purpose
$
0.5 bits
1 bit
capacity gain
(cost)
Send independent backward messages (1)
Net Feedback Gain
Two ways of using backward IC
(2) Send feedback signals for aiding forward-
message tx
Capacity
Gain
(1) First purpose
(2) Feedback purpose
$
0.5 bits
1 bit
Net Gain: 0.5 bits
capacity gain
(cost)
Send independent backward messages (1)
Achievable Scheme
Achievable Scheme
No feedback
Achievable Scheme
No feedback
Achievable Scheme
No feedback
Achievable Scheme
No feedback
Achievable Scheme
Perfect feedback
Achievable Scheme
Time 1
Perfect feedback
Achievable Scheme
Time 1 Time 1
Perfect feedback
Achievable Scheme
decode
Time 1 Time 1
Perfect feedback
Achievable Scheme
decode
decode
Time 1 Time 1
Perfect feedback
Achievable Scheme
decode
decode
Time 1 Time 1 Time 2
Perfect feedback
Achievable Scheme
decode
decode
Time 1 Time 1 Time 2
Perfect feedback
Achievable Scheme
decode
decode
Time 1 Time 1 Time 2 Time 2
Perfect feedback
Achievable Scheme
decode
decode
Time 1 Time 1 Time 2 Time 2
Perfect feedback
Achievable Scheme
decode
decode
Time 1 Time 1 Time 2 Time 2
Perfect feedback
Achievable Scheme
decode
decode
Time 1 Time 1 Time 2 Time 2
Perfect feedback
Achievable Scheme
decode
decode
Time 1 Time 1 Time 2 Time 2
Achievable Scheme
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
want
want
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
Side info
want
want
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
Side info
want
want
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
Side info
want
want
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
Side info
want
want
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
Optimal!
Side info
want
want
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
Optimal!
Side info
want
want
Can feed back 2 bits through 1-bit-capacity backward IC!
Achievable Scheme
Side info
Time 1 Time 1 Time 2 Time 2
Optimal!
Side info
want
want
Can feed back 2 bits through 1-bit-capacity backward IC!
Net feedback gain
Extension: Four-Message Two-way IC
Extension: Four-Message Two-way IC
Interaction provides a significant capacity
increase
Extension: Four-Message Two-way IC
Interaction provides a significant capacity
increase
Mixing forward-&-backward messages
can provide a larger gain
Related Work
Sahai-Aggarwal-Yuksel-Sabharwal `09
Two-way IC with two forward messages
Related Work
Sahai-Aggarwal-Yuksel-Sabharwal `09
No net feedback gain
Two-way IC with two forward messages
Related Work
Sahai-Aggarwal-Yuksel-Sabharwal `09
No net feedback gain
Two-way IC with two forward messages
We consider arbitrary forward-backward ICs
Related Work
No
Gain
?
Net
Gain
Net
Gain
Sahai-Aggarwal-Yuksel-Sabharwal `09
No net feedback gain
Two-way IC with two forward messages
We consider arbitrary forward-backward ICs
Related Work
No
Gain
?
Net
Gain
Net
Gain
Sahai-Aggarwal-Yuksel-Sabharwal `09
No net feedback gain
Two-way IC with two forward messages
Open
We consider arbitrary forward-backward ICs
Conclusion
1
2
3
Conclusion
Sum capacity of two-way IC (except for some channel regimes)
1
2
3
Conclusion
Sum capacity of two-way IC (except for some channel regimes)
A new viewpoint on the use of backward IC
1
2
3
Conclusion
Sum capacity of two-way IC (except for some channel regimes)
A new viewpoint on the use of backward IC
1
2
3
Feedback purpose
Original purpose
(send ind. backward mgs)
>
Conclusion
Sum capacity of two-way IC (except for some channel regimes)
A new viewpoint on the use of backward IC
1
2
3
Feedback purpose
Original purpose
(send ind. backward mgs)
>
side info
no side info
Conclusion
Sum capacity of two-way IC (except for some channel regimes)
A new viewpoint on the use of backward IC
Feedback can provide a net increase in capacity
1
2
3
Feedback purpose
Original purpose
(send ind. backward mgs)
>
side info
no side info
Conclusion
Sum capacity of two-way IC (except for some channel regimes)
A new viewpoint on the use of backward IC
Feedback can provide a net increase in capacity
1
2
3
Feedback purpose
Original purpose
(send ind. backward mgs)
>
side info
no side info
Reference: http://arxiv.org/abs/1202.5014
