1. Ivana Marić, Ron Dabora and Andrea Goldsmith
Relaying in Networks with Multiple Communicating Pairs: Interference Forwarding
Ivana Marić, Ron Dabora and Andrea Goldsmith
Summary
Introduction
Motivation
Channel Model
ACHIEVEMENT DESCRIPTION
Relaying in network with multiple sources has aspects not present in the relay networks:
Relaying messages to one destination increases interference to others
Relays can jointly encode messages from multiple sources
There are many relevant encoding strategies
Encoding strategies for networks with multiple sources are not well understood and developed
Current approach: multihop routing
Time shares between data streams (no joint encoding)
Does not exploit broadcast or interference
We consider smallest network that captures relaying for multiple sources: the interference channel with a relay
Previous work:
Sridharan, Vishwanath, Jafar and Shamai [ISIT, 2008]
Rates and degrees of freedom when the relay is cognitive
Sahin and Erkip [Asilomar 2007, CTW 2008]
Various relaying strategies for forwarding information to intended receivers have been proposed
Capacity of networks are still unknown; one of the key reasons: we don’t know how to handle and exploit interference
In relay networks:
Relays forward data for a single source-destination pair
Cooperative strategies are well developed and known to bring gains
Cooperative strategies exploit the broadcast nature of wireless medium
In networks with multiple sources:
The center issue is coping with interference created by simultaneous transmissions
Networks with multiple sources contain broadcast, multicast, relay and interference channel elements as their building blocks
ASSUMPTIONS AND LIMITATIONS:
To demonstrate interference forwarding gains, we considered scenario in which the relay can observe the signal from only one source and can thus forward only one of the two messages
MAIN RESULT:
We determined conditions under which having a relay enhance the interference improves the performance. We also obtained capacity in the special case
HOW IT WORKS:
The relay forwards a message to a receiver that is not interested in that message, thus increasing the interference at that receiver. This allows the receiver to decode and cancel the interference, and decode its message in the clear channel
dest1
dest2
encoder 1
encoder 2
relay
Compare the rates to outer bounds
Further develop strategies for forwarding in the presence of interference
Consider more general scenarios in which interference enhancement needs to be combined with other relaying strategies
Apply this strategy to larger networks
END-OF-PHASE GOAL
STATUS QUO
Two messages:
Rates:
In networks with multiple sources, relays can help beyond forwarding useful information, by increasing interference at the receivers. This allows receivers to decode the interference and cancel it prior to decoding their desired messages
Encoding:
Decoding:
COMMUNITY CHALLENGE
NEW INSIGHTS
Prize level: Capacity results for networks with multiple sources
We present new relaying strategy: interference forwarding
We proposed a new relaying strategy for networks with multiple sources. We showed that it can improve the rate performance and that it achieves capacity in a certain scenario.
Capacity Result
Gaussian Channels
Assumptions
Achievable Rates
We define strong interference conditions as:
The presence of the relay changes the strong interference conditions
The relay can ‘push’ a receiver into the strong interference regime where decoding of interfering message is optimal
We evaluated these results for the Gaussian channels:
dest1
dest2
encoder 1
encoder 2
relay
Theorem: Any rate pair (R1,R2) that satisfies
(2) ?
satisfied for any distribution p(x1)p(x2,x3)p(y1,y2|x1,x2,x3)
(1)
Conditions (2) are analogous to the strong interference conditions derived by Costa and El Gamal for the interference channel
Conditions (2) imply that the flow of information from each source to the non-intended receiver is better than to the intended receiver
Consequently, receivers can decode the undesired messages for ‘free’ and hence experience no interference
To illustrate gains from interference forwarding, we consider the special case (shown in Figures):
The relay cannot observe signal sent from source 1
Then, it can only forward message W2 thus improving rate R2
From the perspective of the other receiver, the relay is interference forwarding
Can relay help also receiver 1 and improve rate R1?
for any distribution p(x1)p(x2,x3)p(y1,y2|x1,x2,x3)
Noise:
Powers
Rates in the Thm. are achieved by:
Single-user encoding at the encoder 1 to send W1
Decode-and-forward at the encoder 2 and the relay to send message W2
The channel degradedness condition:
(3)
Theorem: When (2)-(3) hold, rates (1) are the capacity region.
In strong interference, decoding both messages is optimal
Insights and Future Work
Comparison with Rate Splitting
Numerical Results for Gaussian Channel
Conclusions
Without the relay, the channel reduces to the interference channel (IC)
The best known rates for IC are achieved with rate splitting:
Demonstrated gains from interference forwarding
Interference forwarding:
Can improve the performance through interference cancellation
Can hurt the receiver by increasing interference
Achieves capacity in a special scenario of strong interference
It ‘pushes’ receiver in strong interference regime where the receiver can decode both messages
We determined conditions under which decoding interference is optimal
Can be realized through decode, compress -and-forward
Can be combined with other encoding schemes
dest1
dest2
encoder 1
encoder 2
relay
Insights:
When relaying for multiple sources:
Jointly encode messages (network coding approach)
Exploit broadcast
Forward messages and interference
Future work:
Develop and evaluate transmission strategies that unify above approaches
Analyze the general case of the interference channel with a relay
Further develop strategies for relaying in the presence of interference
Without the relay: interference channel in strong interference
With relay, h13=0: no interference forwarding
With relay, h13>0: interference forwarding
Interference forwarding enlarges the rate region
It facilitates interference cancellation
In the case when the relay can only use interference forwarding, can the relay still help?
We compare the rates achieved with and without the relay
Proposition: When
strong relay-rcvr1 link
strong source2-relay link
for any distribution p(x1)p(x2,x3)p(y1,y2|x1,x2,x3)
interference forwarding outperforms rate splitting (no relaying).