Repairing a Single Erasure in Reed-Solomon Codes with Side Information

We generalize the problem of recovering a lost/erased symbol in a Reed-Solomon code to the scenario in which some side information about the lost symbol is known. The side information is represented as a set S of linearly independent combinations of the sub-symbols of the lost symbol. When S=\varnot...

Full description

Saved in:
Bibliographic Details
Published in2024 IEEE International Symposium on Information Theory (ISIT) pp. 2122 - 2127
Main Authors Dinh, Thi Xinh, Le, Ba Thong, Dau, Son Hoang, Boztas, Serdar, Kruglik, Stanislav, Kiah, Han Mao, Viterbo, Emanuele, Etzion, Tuvi, Meng Chee, Yeow
Format Conference Proceeding
LanguageEnglish
Published IEEE 07.07.2024
Subjects
Bandwidth
Information theory
Maintenance engineering
Reed-Solomon codes
Symbols
Online AccessGet full text

Cover

More Information
Summary:We generalize the problem of recovering a lost/erased symbol in a Reed-Solomon code to the scenario in which some side information about the lost symbol is known. The side information is represented as a set S of linearly independent combinations of the sub-symbols of the lost symbol. When S=\varnothing , this reduces to the standard problem of repairing a single codeword symbol. When S is a set of sub-symbols of the erased one, this becomes the repair problem with partially lost/erased symbol. We first establish that the minimum repair bandwidth depends on \vert S\vert and not the content of S and construct a lower bound on the repair bandwidth of a linear repair scheme with side information S We then consider the well-known subspace-polynomial repair schemes and show that their repair bandwidths can be optimized by choosing the right subspaces. Finally, we demonstrate several parameter regimes where the optimal bandwidths can be achieved for full-length Reed-Solomon codes.
ISSN:2157-8117
DOI:10.1109/ISIT57864.2024.10619203