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