A Matrix Completion Approach to Linear Index Coding Problem
Homa Esfahanizadeh, Farshad Lahouti, Babak Hassibi
TL;DR
This paper introduces a matrix completion algorithm to optimize transmission rates in linear index coding, applicable to both scalar and vector cases, advancing code design and rate analysis.
Contribution
It presents a novel solution for the minimum rank matrix completion problem over finite fields for linear index coding, enabling optimal rate determination.
Findings
Effective minimum rank matrix completion method developed
Applicable to scalar and vector linear index coding
Enhances rate analysis and code design efficiency
Abstract
In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding problem is devised in order to find the optimum transmission rate given vector length and size of the field. The new approach can be applied to both scalar and vector linear index coding.
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