Index coding via linear programming
Anna Blasiak, Robert Kleinberg, Eyal Lubetzky

TL;DR
This paper introduces a linear programming approach to analyze and approximate the broadcast rate in Index Coding, providing polynomial algorithms and exact values for specific graph classes, thus advancing understanding of the problem's complexity and bounds.
Contribution
It presents a direct linear programming method for analyzing the broadcast rate, enabling polynomial-time approximation and exact recognition of certain instances, which was previously unresolved.
Findings
Polynomial-time algorithm approximates the broadcast rate within a nontrivial factor.
Polynomial-time decision procedure identifies instances with broadcast rate 2.
Exact broadcast rate determined for various Cayley graph classes.
Abstract
Index Coding has received considerable attention recently motivated in part by real-world applications and in part by its connection to Network Coding. The basic setting of Index Coding encodes the problem input as an undirected graph and the fundamental parameter is the broadcast rate , the average communication cost per bit for sufficiently long messages (i.e. the non-linear vector capacity). Recent nontrivial bounds on were derived from the study of other Index Coding capacities (e.g. the scalar capacity ) by Bar-Yossef et al (2006), Lubetzky and Stav (2007) and Alon et al (2008). However, these indirect bounds shed little light on the behavior of : there was no known polynomial-time algorithm for approximating in a general network to within a nontrivial (i.e. ) factor, and the exact value of remained unknown for any graph where…
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Taxonomy
TopicsCooperative Communication and Network Coding · Caching and Content Delivery · Wireless Communication Security Techniques
