Optimal dual pairs of frames for erasures

2024/12/20 by S. Arati, Arati, S., P. Devaraj +3 · 2 citations
Computer Science · Engineering · Mathematics · #15A60 #42C15 #46C05 #Advanced Harmonic Analysis Research #Coding theory and cryptography #FOS: Mathematics #Functional Analysis (math.FA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2412.15709

openalex publication_date 2024/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study involves characterizations of dual pairs of frames which are optimal to handle erasures among all dual pairs for a finite dimensional Hilbert space. A new optimality measure using the Frobenius norm of the error operator has been introduced and the corresponding optimal dual pairs have been analyzed for any number of erasures. Also, other measures of the error operator, namely the spectral radius and the numerical radius, have been considered for the analysis. Besides, explicit construction of certain optimal dual pairs has been provided.

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• Optimal Dual Frame Pairs: A Synergy with Graph Theory
• On the paper Optimal dual frames of probabilistic erasures

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