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33
Topological interference management through index coding
, 2013
"... While much recent progress on interference networks has come about under the assumption of abundant channel state information at the transmitters (CSIT), a complementary perspective is sought in this work through the study of interference networks with no CSIT except a coarse knowledge of the topolo ..."
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Cited by 30 (14 self)
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While much recent progress on interference networks has come about under the assumption of abundant channel state information at the transmitters (CSIT), a complementary perspective is sought in this work through the study of interference networks with no CSIT except a coarse knowledge of the topology of the network that only allows a distinction between weak and significant channels and no further knowledge of the channel coefficients ’ realizations. Modeled as a degrees-of-freedom (DoF) study of a partially connected interference network with no CSIT, the problem is found to have a counterpart in the capacity analysis of wired networks with arbitrary linear network coding at intermediate nodes, under the assumption that the sources are aware only of the end to end topology of the network. The wireless (wired) network DoF (capacity) region, expressed in dimensionless units as a multiple of the DoF (capacity) of a single point to point channel (link), is found to be bounded above by the capacity of an index coding problem where the antidotes graph is the complement of the interference graph of the original network and the bottleneck link capacity is normalized to unity. The problems are shown to be equivalent under linear solutions over the same field. An interference alignment
On the capacity region for index coding
- IN PROC. IEEE INT. SYMP. INF. THEORY
, 2013
"... A new inner bound on the capacity region of the general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound relies on a random coding scheme and optimal decoding, and has a simple polymatroidal single-letter expression. Th ..."
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Cited by 13 (5 self)
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A new inner bound on the capacity region of the general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound relies on a random coding scheme and optimal decoding, and has a simple polymatroidal single-letter expression. The utility of the inner bound is demonstrated by examples that include the capacity region for all index coding problems with up to five messages (there are 9846 nonisomorphic ones).
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.
Instantly Decodable Network Codes for Real-Time Applications
"... We consider the scenario of broadcasting for real-time applications and loss recovery via instantly decodable network coding. Past work focused on minimizing the completion delay, which is not the right objective for real-time applications that have strict deadlines. In this work, we are interested ..."
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Cited by 9 (0 self)
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We consider the scenario of broadcasting for real-time applications and loss recovery via instantly decodable network coding. Past work focused on minimizing the completion delay, which is not the right objective for real-time applications that have strict deadlines. In this work, we are interested in finding a code that is instantly decodable by the maximum number of users. First, we prove that this problem is NP-Hard in the general case. Then we consider the practical probabilistic scenario, where users have i.i.d. loss probability, and the number of packets is linear or polynomial in the number of users. In this case, we provide a polynomial-time (in the number of users) algorithm that finds the optimal coded packet. Simulation results show that the proposed coding scheme significantly outperforms an optimal repetition code and a COPE-like greedy scheme.
Optimal index codes with near-extreme rates
- in Proc. IEEE Int. Symp. Inf. Theory
, 2012
"... Abstract—The min-rank of a digraph was shown by Bar-Yossef et al. (2006) to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this work, the graphs and digraphs of near-extreme min-ranks are characteri ..."
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Cited by 8 (0 self)
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Abstract—The min-rank of a digraph was shown by Bar-Yossef et al. (2006) to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this work, the graphs and digraphs of near-extreme min-ranks are characterized. Those graphs and digraphs correspond to the ICSI instances having near-extreme transmission rates when using optimal scalar linear index codes. It is also shown that the decision problem of whether a digraph has min-rank two is NP-complete. By contrast, the same question for graphs can be answered in polynomial time. I.
Elements of Cellular Blind Interference Alignment — Aligned Frequency Reuse
- Wireless Index Coding and Interference Diversity”, March 2012, e-print arXiv:1203.2384
"... We explore degrees of freedom (DoF) characterizations of partially connected wireless net-works, especially cellular networks, with no channel state information at the transmitters. Specifically, we introduce three fundamental elements — aligned frequency reuse, wireless in-dex coding and interferen ..."
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Cited by 7 (3 self)
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We explore degrees of freedom (DoF) characterizations of partially connected wireless net-works, especially cellular networks, with no channel state information at the transmitters. Specifically, we introduce three fundamental elements — aligned frequency reuse, wireless in-dex coding and interference diversity — through a series of examples, focusing first on infinite regular arrays, then on finite clusters with arbitrary connectivity and message sets, and finally on heterogeneous settings with asymmetric multiple antenna configurations. Aligned frequency reuse refers to the optimality of orthogonal resource allocations in many cases, but according to unconventional reuse patterns that are guided by interference alignment principles. Wireless index coding highlights both the intimate connection between the index coding problem and cellular blind interference alignment, as well as the added complexity inherent to wireless set-tings. Interference diversity refers to the observation that in a wireless network each receiver experiences a different set of interferers, and depending on the actions of its own set of interfer-ers, the interference-free signal space at each receiver fluctuates differently from other receivers, creating opportunities for robust applications of blind interference alignment principles. ar X iv
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 non-Shannon 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 non-Shannon 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 non-Shannon 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 non-Shannon 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.
Secure Degrees of Freedom of MIMO X-Channels With Output Feedback and Delayed CSIT
- IEEE Transactions on Information Forensics and Security
, 2013
"... ar ..."
On the Capacity of the Finite Field Counterparts of Wireless Interference Networks
, 2013
"... This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over Fpn are analogous ..."
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Cited by 5 (3 self)
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This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over Fpn are analogous to n × n vector (MIMO) channels in the wireless setting, but with an important distinction – there is additional structure due to finite field arithmetic which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts. This is shown through the study of capacity of the 2-user X channel and linear capacity of the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over Fpn also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity.
