Defect tolerance: fundamental limits and examples
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defects.pdf
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Accepted version
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503.42 KB
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af7365b0f03d2948a6775f8b4a910d3d
Author(s)
Tang, Jennifer Susan
Wang, Da
Polyanskiy, Yury
Wornell, Gregory
Date Issued
July 2018
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Tang, Jennifer Susan, Da Wang, Yury Polyanskiy, and Gregory Wornell, "Defect tolerance: fundamental limits and examples." IEEE Transactions on Information Theory 64, 7 (July 2018): p. 5240-60 doi 10.1109/TIT.2017.2771417 ©2018 Author(s)
Version
Author's final manuscript
Abstract
This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple information symbols from a single erasure, physical redundancy can only be realized through duplication and substitution of objects. We propose a bipartite graph model for designing defect-tolerant systems, in which the defective objects are replaced by the judiciously connected redundant objects. The fundamental limits of this model are characterized under various asymptotic settings and both asymptotic and finite-size systems that approach these limits are constructed. Among other results, we show that the simple modular redundancy is in general suboptimal. As we develop, this combinatorial problem of defect tolerant system design has a natural interpretation as one of graph coloring, and the analysis is significantly different from that traditionally used in information redundancy for error-control codes.©2018
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/TIT.2017.2771417
