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30
Index coding: An interference alignment perspective
 in International Symposium on Information Theory
, 2012
"... The index coding problem is studied from an interference alignment perspective providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between the capacity of the multiple unicast index coding (where each message is desired ..."
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Cited by 32 (9 self)
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The index coding problem is studied from an interference alignment perspective providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between the capacity of the multiple unicast index coding (where each message is desired by exactly one receiver), and groupcast index coding (where a message can be desired by multiple receivers), which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings where this question has previously been answered. Necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints, and generalizations to feasibility of rate 1 L+1 per message when each destination desires at least L messages, are similarly obtained. Finally, capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks. The solutions are based on vector linear coding.
Topological interference management with alternating connectivity
 Online]. Available: http://arxiv.org/abs/1302.4020
, 2013
"... Abstract—The topological interference management problem refers to the study of the capacity of partially connected linear (wired and wireless) communication networks with no channel state information at the transmitters (no CSIT) beyond the network topology, i.e., a knowledge of which channel coeff ..."
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Cited by 10 (2 self)
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Abstract—The topological interference management problem refers to the study of the capacity of partially connected linear (wired and wireless) communication networks with no channel state information at the transmitters (no CSIT) beyond the network topology, i.e., a knowledge of which channel coefficients are zero (weaker than the noise floor in the wireless case). While the problem is originally studied with fixed topology, in this work we explore the implications of varying connectivity, through a series of simple and conceptually representative examples. Specifically, we highlight the synergistic benefits of coding across alternating topologies. I.
Aligned image sets under channel uncertainty: Settling a conjecture by lapidoth, shamai and wigger on the collapse of degrees of freedom under finite precision csit,” arXiv preprint arXiv:1403.1541
"... A conjecture made by Lapidoth, Shamai and Wigger at Allerton 2005 (also an open problem presented at ITA 2006) states that the degrees of freedom (DoF) of a two user broadcast channel, where the transmitter is equipped with 2 antennas and each user is equipped with 1 antenna, must collapse under fin ..."
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Cited by 8 (1 self)
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A conjecture made by Lapidoth, Shamai and Wigger at Allerton 2005 (also an open problem presented at ITA 2006) states that the degrees of freedom (DoF) of a two user broadcast channel, where the transmitter is equipped with 2 antennas and each user is equipped with 1 antenna, must collapse under finite precision channel state information at the transmitter (CSIT). That this conjecture, which predates interference alignment, has remained unresolved, is emblematic of a pervasive lack of understanding of the degrees of freedom of wireless networks—including interference and X networks—under channel uncertainty at the transmitter(s). In this work we prove that the conjecture is true in all nondegenerate settings (e.g., where the probability density function of unknown channel coefficients exists and is bounded). The DoF collapse even when perfect channel knowledge for one user is available to the transmitter. This also settles a related recent conjecture by Tandon et al. The key to our proof is a bound on the number of codewords that can cast the same image (within noise distortion) at the undesired receiver whose channel is subject to finite precision CSIT, while remaining resolvable at the desired receiver whose channel is precisely known by the transmitter. We are also able to generalize the result
Index coding capacity: How far can one go with only Shannon inequalities?
, 2015
"... An interference alignment perspective is used to identify the simplest instances (minimum possible number of edges in the alignment graph, not more than 2 interfering messages at any destination) of index coding problems where nonShannon information inequalities are necessary for capacity characte ..."
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Cited by 7 (1 self)
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An interference alignment perspective is used to identify the simplest instances (minimum possible number of edges in the alignment graph, not more than 2 interfering messages at any destination) of index coding problems where nonShannon information inequalities are necessary for capacity characterization. In particular, this includes the first known example of a multiple unicast (one destination per message) index coding problem where nonShannon information inequalities are shown to be necessary. The simplest multiple unicast example has 7 edges in the alignment graph and 11 messages. The simplest multiple groupcast (multiple destinations per message) example has 6 edges in the alignment graph, 6 messages, and 10 receivers. For both the simplest multiple unicast and multiple groupcast instances, the best outer bound based on only Shannon inequalities is 2/5, which is tightened to 11/28 by the use of the Zhang–Yeung nonShannon type information inequality, and the linear capacity is shown to be 5/13 using the Ingleton inequality. Conversely, identifying the minimal challenging aspects of the index coding problem allows an expansion of the class of solved index coding problems up to (but not including) these instances.
Order optimal coded cachingaided multicast under zipf demand distributions,” arXiv preprint arXiv:1402.4576
, 2014
"... Abstract—Caching and multicasting are two key technologies for reducing traffic load in content delivery networks. While uncoded caching based delivery schemes can offer competitive performance under skewed popularity distributions, the use of coded transmission schemes of increased complexity has b ..."
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Cited by 4 (1 self)
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Abstract—Caching and multicasting are two key technologies for reducing traffic load in content delivery networks. While uncoded caching based delivery schemes can offer competitive performance under skewed popularity distributions, the use of coded transmission schemes of increased complexity has been recently shown to significantly improve multicast efficiency under flatter popularity distributions, by exploiting coded multicast opportunities created by simple cooperative caching policies. In this paper, we consider a caching network with one source, hosting m files, connected to n destinations, each with a storage capacity of M files, via a shared link. Given that file requests follow a Zipf popularity distribution, our objective is to characterize the minimum average number of transmissions to satisfy all user demands in the information theoretic sense. We present both achievable coded cachingaided multicast schemes and outer bounds for this network configuration and show that as m,n → ∞, for any M, the achievable average number of transmissions and the outer bound meets up to a constant factor. Index Terms—Multicast, caching, network coding, index coding, content distribution. I.
Optimality of orthogonal access for onedimensional convex cellular networks
, 2013
"... It is shown that a greedy orthogonal access scheme achieves the sum degrees of freedom of all onedimensional (all nodes placed along a straight line) convex cellular networks (where cells are convex regions) when no channel knowledge is available at the transmitters except the knowledge of the netw ..."
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Cited by 3 (1 self)
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It is shown that a greedy orthogonal access scheme achieves the sum degrees of freedom of all onedimensional (all nodes placed along a straight line) convex cellular networks (where cells are convex regions) when no channel knowledge is available at the transmitters except the knowledge of the network topology. In general, optimality of orthogonal access holds neither for twodimensional convex cellular networks nor for onedimensional nonconvex cellular networks, thus revealing a fundamental limitation that exists only when both onedimensional and convex properties are simultaneously enforced, as is common in canonical information theoretic models for studying cellular networks. The result also establishes the capacity of the corresponding class of index coding problems.
Topological interference management with alternating connectivity: The Wynertype three user interference channel.” [Online]. Available: http://arxiv.org/ abs/1310.2385
, 2013
"... Abstract—Interference management in a threeuser interference channel with alternating connectivity with only topological knowledge at the transmitters is considered. The network has a Wynertype channel flavor, i.e., for each connectivity state the receivers observe at most one interference signal ..."
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Cited by 3 (1 self)
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Abstract—Interference management in a threeuser interference channel with alternating connectivity with only topological knowledge at the transmitters is considered. The network has a Wynertype channel flavor, i.e., for each connectivity state the receivers observe at most one interference signal in addition to their desired signal. Degrees of freedom (DoF) upper bounds and lower bounds are derived. The lower bounds are obtained from a scheme based on joint encoding across the alternating states. Given a uniform distribution among the connectivity states, it is shown that the channel has 2+1/9 DoF. This provides an increase in the DoF as compared to encoding over each state separately, which achieves 2 DoF only. I.
Local Time Sharing for Index Coding
"... Abstract—A series of extensions of the index coding schemes based on time sharing by Birk and Kol, by Blasiak, Kleinberg, and Lubetzky, and by Shanmugam, Dimakis, and Langberg are presented. Each extension strictly improves upon the previous extensions as well as the existing schemes. The main idea ..."
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Cited by 3 (2 self)
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Abstract—A series of extensions of the index coding schemes based on time sharing by Birk and Kol, by Blasiak, Kleinberg, and Lubetzky, and by Shanmugam, Dimakis, and Langberg are presented. Each extension strictly improves upon the previous extensions as well as the existing schemes. The main idea behind these extensions is local time sharing over subproblems introduced by Shanmugam et al., in which the local side information available at each receiver is exploited to send the subproblm indices with a fewer number of transmissions. The final extension, despite being the best in this class of coding schemes, is shown to be still suboptimal, characterizing the fundamental limit of local time sharing. I.
Fundamental Limits of Caching in Wireless D2D Networks
, 2014
"... We consider a wireless DevicetoDevice (D2D) network where communication is restricted to be singlehop. Users make arbitrary requests from a finite library of files and have precached information on their devices, subject to a pernode storage capacity constraint. A similar problem has already be ..."
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Cited by 2 (0 self)
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We consider a wireless DevicetoDevice (D2D) network where communication is restricted to be singlehop. Users make arbitrary requests from a finite library of files and have precached information on their devices, subject to a pernode storage capacity constraint. A similar problem has already been considered in an “infrastructure ” setting, where all users receive a common multicast (coded) message from a single omniscient server (e.g., a base station having all the files in the library) through a shared bottleneck link. In this work, we consider a D2D “infrastructureless ” version of the problem. We propose a caching strategy based on deterministic assignment of subpackets of the library files, and a coded delivery strategy where the users send linearly coded messages to each other in order to collectively satisfy their demands. We also consider a random caching strategy, which is more suitable to a fully decentralized implementation. Under certain conditions, both approaches can achieve the information theoretic outer bound within a constant multiplicative factor. In our previous work, we showed that a caching D2D wireless network with onehop communication, random caching, and uncoded delivery (direct file transmissions), achieves the same throughput scaling law of the infrastructurebased coded multicasting scheme, in the regime of large number of users and
Bounding multiple unicasts through index coding and locally repairable codes
 In Information Theory Proceedings (ISIT), 2014 IEEE International Symposium on
, 2014
"... Abstract—We establish a duality result between linear index ..."
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Abstract—We establish a duality result between linear index