Conference Paper

# Index Coding with Side Information

Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa

DOI: 10.1109/FOCS.2006.42 Conference: Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on Source: IEEE Xplore

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**ABSTRACT:**A full-duplex wireless network with three users that want to establish full message exchange via a relay is considered. Thus, this network which is known as the Y-channel has a total of six messages, two outgoing, and two incoming at each user. The users are not physically connected, and thus the relay is essential for their communication. The deterministic Y-channel is considered first, its capacity region is characterized, and shown not to be given by the cut-set bounds. The capacity achieving scheme has three different components (strategies): 1) a bidirectional; 2) a cyclic; and 3) a unidirectional strategy. Network coding is used to realize the bidirectional and the cyclic strategies, and thus to prove the achievability of the capacity region. The result is then extended to the Gaussian Y-channel where the capacity region is characterized within a constant gap independent of the channel parameters.IEEE Transactions on Information Theory 01/2015; 61(2):939 - 962. · 2.65 Impact Factor -
##### Article: Topological Interference Management with just Retransmission: What are the "Best" Topologies?

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**ABSTRACT:**We study the problem of interference management in fast fading wireless networks, in which the transmitters are only aware of network topology. We consider a class of retransmission-based schemes, where transmitters in the network are only allowed to resend their symbols in order to assist with the neutralization of interference at the receivers. We introduce a necessary and sufficient condition on the network topology, under which half symmetric degrees-of-freedom (DoF) is achievable through the considered retransmission-based schemes. This corresponds to the "best" topologies since half symmetric DoF is the highest possible value for the symmetric DoF in the presence of interference. We show that when the condition is satisfied, there always exists a set of carefully chosen transmitters in the network, such that by retransmission of their symbols at an appropriate time slot, we can neutralize all the interfering signals at the receivers. Quite surprisingly, we also show that for any given network topology, if we cannot achieve half symmetric DoF by retransmission-based schemes, then there does not exist any linear scheme that can do so. We also consider a practical network scenario that models cell edge users in a heterogeneous network, and show that the characterized condition on the network topology occurs frequently. Furthermore, we numerically evaluate the achievable rates of the DoF-optimal retransmission-based scheme in such network scenario, and show that its throughput gain is not restricted to the asymptotic DoF analysis.02/2015; - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side information of the first message. We make three contributions in this paper: 1. We describe a new linear network coding algorithm for two-unicast-Z networks over directed acyclic graphs. Our approach includes the idea of interference alignment as one of its key ingredients. For graphs of a bounded degree, our algorithm has linear complexity in terms of the number of vertices, and polynomial complexity in terms of the number of edges. 2. We prove that our algorithm achieves the rate-pair (1, 1) whenever it is feasible in the network. Our proof serves as an alternative, albeit restricted to two-unicast-Z networks over directed acyclic graphs, to an earlier result of Wang et al. which studied necessary and sufficient conditions for feasibility of the rate pair (1, 1) in two-unicast networks. 3. We provide an new proof of the classical max-ow min-cut theorem for directed acyclic graphs.02/2015;

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