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Relaying in networks with multiple sources has new aspects: 1. Relaying messages to one destination increases interference to others 2. Relays can jointly encode messages from multiple sources Many relevant encoding strategies exist Current approach: multihop routing Time shares between data streams (no joint encoding) Does not exploit broadcast or interference We consider smallest such network: the interference channel with a relay (ICR) Related work: Sridharan, Vishwanath, Jafar and Shamai [ISIT 2008]: Rates and degrees of freedom when the relay is cognitive Sahin and Erkip [Asilomar 2007, 2008] Comparisons Performance Bounds for the Interference Channel with a Relay Ivana Marić, Ron Dabora and Andrea Goldsmith Developed a sum-rate outer bound for Gaussian channels Demonstrated that the bound can be significantly tighter than the cut-set bound and than the existing cognitive ICR bounds The bound is close to the achievable rates in the strong interference regime Encoding: Decoding: Two messages: Channel Model ? A genie-added approach for an interference channel outer bound extended to the interference channel with a relay. Genie gives a receiver noisy inputs from sources and the relay. Although inputs are dependent (unlike in interference channels), one can still optimize inputs to obtain a bound. Several relaying strategies for forwarding information to a single receiver exist Capacity of networks are still unknown; one of the key obstacles: how to handle and exploit interference? What is the performance when relaying for multiple sources? A sum-rate outer bound for the Gaussian interference channel with a relay developed. IMPACT NEXT-PHASE GOALS ACHIEVEMENT DESCRIPTION Motivation In relay networks: Relays forward data for a single source-destination pair Cooperative strategies improve performance and exploit the broadcast nature of wireless medium In networks with multiple sources: The center issue is coping with interference created by simultaneous transmissions A relay helping one destination can hurt others Networks with multiple sources contain broadcast, multicast, relay and interference channels STATUS QUO NEW INSIGHTS MAIN ACHIEVEMENT: A new sum-rate outer bound to the performance of the Gaussian interference channel with a relay HOW IT WORKS: A genie gives to a receiver minimum information needed for decoding both messages ASSUMPTIONS AND LIMITATIONS: The considered channel model: the interference channel with a relay The genie cannot be turned-off even when not needed i.e., in strong interference regime. 1)Tighter outer bound than cut-set bound and than existing cognitive ICR bounds 2)Close to achievable rates in strong interference Apply interference forwarding and the outer bound approach to larger networks Introduction Capacity Result in Strong Interference Conclusions and Future Work A New Sum-Rate Outer Bound for Gaussian Channels We have previously proposed a coding scheme for the ICR and derived achievable rates We have shown that interference forwarding can improve performance by facilitating interference cancellation The relay ‘pushes’ a receiver into the strong interference regime where decoding an interfering message is optimal This can hurt a receiver if increased interference is not strong enough for decoding Future work: Limitation of the approach: both decoders decode both messages A genie technique recently developed for ICs may overcome this problem Challenge: determining optimal channel inputs For ICs: Gaussian inputs are optimal Apply and analyze interference forwarding and the genie-added approach employed in this outer bound to larger networks We define strong interference conditions as: Analogous to the strong interference conditions by Costa and El Gamal for interference channels (IC) (2) imply that the flow of information from each source to the non- intended receiver is better than to the intended receiver Then, receivers can decode undesired messages for any distribution p(x 1 )p(x 2 )p(x 3 |x 1 x 2 )p(y 1,y 2 |x 1,x 2,x 3 ) The channel degradedness condition: Theorem: When (2)-(3) hold, rates (1) are the capacity region. In strong interference, decoding both messages is optimal Gaussian channels:DMCs: Noise: Powers Rates: (2) (3) Summary Extend the approach developed for Gaussian interference channels by [Kramer 2004] A genie gives to a receiver minimum information about source and relay inputs needed for decoding both messages Receiver 1 can form an estimate: Maximized by jointly Gaussian inputs The sum-rate is upper bounded by for parameter values for which receiver 1 can decode W 2 One can show that -> When var( Z e )`
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