Erasure Recovery Matrices for Data Erasures and Rearrangements

Miao He (), Changtian Wu and Jinsong Leng
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Miao He: School of Mathematics and Physics, Chengdu University of Technology, Chengdu 611731, China
Changtian Wu: School of Mathematics and Physics, Chengdu University of Technology, Chengdu 611731, China
Jinsong Leng: School of Mathematical and Sciences, University of Electronic Science and Technology of China, Chengdu 610059, China

Mathematics, 2024, vol. 12, issue 7, 1-16

Abstract: When studying signal reconstruction, the frames are often selected in advance as encoding tools. However, in practical applications, this encoding frame may be subject to attacks by intermediaries and generate errors. To solve this problem, in this paper, the erasure recovery matrices for data erasures and rearrangements are analyzed. Unlike the previous research, first of all, we introduce a kind of frame and its erasure recovery matrix M so that M I , Λ = I m × m , where I m × m is a unit matrix. In this case, we do not need to invert the matrix of the frame operator and the erasure recovery matrix, and this greatly simplifies reconstruction problems and calculations. Then three different construction algorithms of the above erasure recovery matrix M and the frame are proposed, and each of them has advantages. Furthermore, some restrictions on M so that the constructed frame and erasure recovery matrix M can recover coefficients from rearrangements are imposed. We prove that in some cases, the above M and frame can recover coefficients stably from m rearrangements.

Keywords: frames; erasure recovery matrices; erasures; rearrangements (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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