Upper Bounds on the Size of Grain-Correcting Codes
Navin Kashyap, Gilles Z\'emor
TL;DR
This paper establishes new upper bounds on the size of binary codes capable of correcting errors in high-density magnetic recording, considering the grain boundary error model.
Contribution
It introduces improved upper bounds on code size and rate for grain-correcting codes in magnetic recording, refining previous combinatorial error models.
Findings
New upper bounds on code cardinality
Enhanced understanding of error correction limits
Refined theoretical limits for magnetic recording codes
Abstract
In this paper, we re-visit the combinatorial error model of Mazumdar et al. that models errors in high-density magnetic recording caused by lack of knowledge of grain boundaries in the recording medium. We present new upper bounds on the cardinality/rate of binary block codes that correct errors within this model.
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Taxonomy
TopicsAlgorithms and Data Compression · Cellular Automata and Applications · DNA and Biological Computing