Index Coding - An Interference Alignment Perspective

Abstract

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 multiple unicast index coding where each message is desired by exactly one receiver, and multiple 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 multiple groupcast settings where this question has previously been answered. Necessary and sufficient conditions for the achievability of rate half per message are shown to be a natural consequence of interference alignment constraints, and generalizations to feasibility of rate $\frac{1}{L+1}$ 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.

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• Index coding via linear programming
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• On Equivalence Between Network Topologies
• Network Coding for Multiple Unicasts: An Interference Alignment Approach
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Cited by in corpus (12)

• Topological Interference Management through Index Coding
• Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT
• Local Graph Coloring and Index Coding
• Index Coding Capacity: How far can one go with only Shannon Inequalities?
• Topological Interference Management with Alternating Connectivity
• Multi-Way Information Exchange Over Completely-Connected Interference Networks with a Multi-Antenna Relay
• Space-Time Interference Alignment and Degrees of Freedom Regions for the MISO Broadcast Channel with Periodic CSI Feedback
• Network Codes for Real-Time Applications
• Topological Interference Management with Transmitter Cooperation
• Index Coding and Network Coding via Rank Minimization
• Index Coding Problem with Side Information Repositories
• Optimality of Orthogonal Access for One-dimensional Convex Cellular Networks