Relaying in networks with multiple sources has new aspects:

1. Noise: Powers Performance Bounds for the Interference Channel with a Relay Ivana Marić, Ron Dabora and Andrea Goldsmith Summary Introduction Motivation ACHIEVEMENT DESCRIPTION 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? • 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 • Relaying in networks with multiple sources has new aspects: • Relaying messages to one destination increases interference to others • 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] • 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. • 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 • Tighter outer bound than cut-set bound and than existing cognitive ICR bounds • Close to achievable rates in strong interference IMPACT STATUS QUO 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. NEW INSIGHTS • Apply interference forwarding and the outer bound approach to larger networks NEXT-PHASE GOALS A sum-rate outer bound for the Gaussian interference channel with a relay developed. Comparisons A New Sum-Rate Outer Bound for Gaussian Channels Channel Model • 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 • We choose parameters so that receiver 1 gets less noisy observation about W2 than receiver2 • Gaussian channels: DMCs: -> When var( Ze )<var( Z2 )receiver 1 can decode (W1,W2) ? • One can show that • Maximized by jointly Gaussian inputs • Two messages: • The sum-rate is upper bounded by • Rates: • The new bound tighter than the cut-set bound for parameter values for which receiver 1 can decode W2 • Encoding: • Receiver 1 can form an estimate: • Decoding: • The new bound tighter than bounds for cognitive ICR • Close to achievable rates in strong interference Capacity Result in Strong Interference Conclusions and Future Work • We define strong interference conditions as: • Also obtained strong interference conditions for our proposed encoding scheme • Proposed encoding scheme: • Gaussian inputs • Encoders split power between sending new data and cooperating with the relay • The relay splits its power to cooperate with both pairs • We obtain strong interference conditions as: • 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 (2) • 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 for any distribution p(x1)p(x2)p(x3 |x1x2)p(y1,y2|x1,x2,x3) • 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 (3) • The channel degradedness condition: • Theorem: When (2)-(3) hold, rates (1) are the capacity region. • In strong interference, decoding both messages is optimal