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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.
Topological Interference Management for Hexagonal Cellular Networks
"... Abstract—We consider the topological interference manage-ment problem for a downlink hexagonal cellular network, where the channel state information at the transmitters is limited to just the network topology. Recent work by Jafar showed that if interference is limited to only near the cell boundary ..."
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Abstract—We consider the topological interference manage-ment problem for a downlink hexagonal cellular network, where the channel state information at the transmitters is limited to just the network topology. Recent work by Jafar showed that if interference is limited to only near the cell boundary, then, an aligned frequency reuse pattern achieves the optimal value of 6/7 degrees of freedom (DoF) per cell, as opposed to the conventional frequency reuse baseline of 1/3 DoF per cell. We generalize the setting to include interference from multiple layers of adjacent cells and characterize how the gains of the optimal solution over basic frequency reuse diminish with increasing number of interfer-ence layers. Next, we focus on single-layer interference and explore the sensitivity of the idealized assumptions behind the connectivity model of Jafar, which achieves higher DoF but only at the cost of a higher effective noise floor than the baseline, and under idealized placements of users. A modified connectivity model that operates at a comparable noise-floor to the baseline is then studied, and its DoF are shown to be bounded above by 6/11 and below by 1/2. Through numerical simulations, we compare the solutions that achieve 6/7, 1/2, and 1/3 DoF per cell and find that, while both the 6/7 and the 1/2 DoF solutions beat the baseline 1/3 figure, between them, the 1/2 DoF aligned frequency reuse pattern is more robust for small cell networks particularly for random users ’ distribution on the cell boundaries. Index Terms—Hexagonal cellular network, degree of freedom, aligned frequency reuse, topological interference management. I.
Index Coding and Network Coding via Rank Minimization
"... Abstract—Index codes reduce the number of bits broadcast by a wireless transmitter to a number of receivers with different demands and with side information. It is known that the problem of finding optimal linear index codes is NP-hard. We investigate the performance of different heuristics based on ..."
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Abstract—Index codes reduce the number of bits broadcast by a wireless transmitter to a number of receivers with different demands and with side information. It is known that the problem of finding optimal linear index codes is NP-hard. We investigate the performance of different heuristics based on rank minimization and matrix completion methods, such as alternating projections and alternating minimization, for constructing linear index codes over the reals. As a summary of our results, the alternating projections method gives the best results in terms of minimizing the number of broadcast bits and convergence rate and leads to up to 13 % savings in average communication cost compared to graph coloring algorithms studied in the literature. Moreover, we describe how the proposed methods can be used to construct linear network codes for non-multicast networks. Our computer code is available online. I.
Blind Interference Alignment in General Heterogeneous Networks
"... Abstract—Heterogeneous networks have a key role in the design of future mobile communication networks, since the employment of small cells around a macrocell enhances the net-work’s efficiency and decreases complexity and power demand. Moreover, research on Blind Interference Alignment (BIA) has sho ..."
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Abstract—Heterogeneous networks have a key role in the design of future mobile communication networks, since the employment of small cells around a macrocell enhances the net-work’s efficiency and decreases complexity and power demand. Moreover, research on Blind Interference Alignment (BIA) has shown that optimal Degrees of Freedom (DoF) can be achieved in certain network architectures, with no requirement of Channel State Information (CSI) at the transmitters. Our contribution is a generalised model of BIA in a heterogeneous network with one macrocell with K users and K femtocells each with one user, by using Kronecker (Tensor) Product representation. We introduce a solution on how to vary beamforming vectors under power constraints to maximize the sum rate of the network and how optimal DoF can be achieved over K + 1 time slots. I.
1Diophantine Approach to Blind Interference Alignment of Homogeneous K-user 2 × 1 MISO Broadcast Channels
"... Although the sufficient condition for a blindly interference-aligned (BIA) 2-user 2 × 1 broadcast channel (BC) in homogeneous fading to achieve its maximal 4/3 DoF is well understood, its counterpart for the general K-user 2 × 1 MISO BC in homogeneous block fading to achieve the corresponding 2K2+K− ..."
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Although the sufficient condition for a blindly interference-aligned (BIA) 2-user 2 × 1 broadcast channel (BC) in homogeneous fading to achieve its maximal 4/3 DoF is well understood, its counterpart for the general K-user 2 × 1 MISO BC in homogeneous block fading to achieve the corresponding 2K2+K−1 (DoF) remains unsolved and is, thus, the focus of this paper. An interference channel is said BIA-feasible if it achieves its maximal DoF only via BIA. In this paper, we cast this general feasibility problem in the framework of finding integer solutions for a system of linear Diophantine equations. By assuming independent user links each of the same coherence time and by studying the solvability of the Diophantine system, we derive the sufficient and necessary conditions on the K users ’ fading block offsets to ensure the BIA feasibility of the K-user BC. If the K offsets are independent and uniformly distributed over a coherence block, we can further prove that 11 users are enough for one to find, with certainty of 95%, 3 users among them to form a BIA-feasible 3-user 2 × 1 BC.
1Interference Networks with No CSIT: Impact of Topology
"... We consider partially-connected K-user interference networks, where the transmitters have no knowl-edge about the channel gain values, but they are aware of network topology (or connectivity). We introduce several linear algebraic and graph theoretic concepts to derive new topology-based outer bound ..."
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We consider partially-connected K-user interference networks, where the transmitters have no knowl-edge about the channel gain values, but they are aware of network topology (or connectivity). We introduce several linear algebraic and graph theoretic concepts to derive new topology-based outer bounds and inner bounds on the symmetric degrees-of-freedom (DoF) of these networks. We evaluate our bounds for two classes of networks to demonstrate their tightness for most networks in these classes, quantify the gain of our inner bounds over benchmark interference management strategies, and illustrate the effect of network topology on these gains. I.
