Title :
Bounds and Constructions for Granular Media Coding
Author :
Sharov, Artyom ; Roth, Ron M.
Author_Institution :
Comput. Sci. Dept., Technion - Israel Inst. of Technol., Haifa, Israel
Abstract :
Bounds on the rates of grain-correcting codes are presented. The lower bounds are Gilbert-Varshamov-like ones, whereas the upper bounds improve on the previously known result by Mazumdar Constructions of t-grain-correcting codes of length n for certain values of n and t are discussed. Finally, an infinite family of codes of rate approaching 1 that can detect an arbitrary number of grain errors is shown to exist.
Keywords :
error analysis; error correction codes; estimation theory; Gilbert-Varshamov-like ones; Mazumdar constructions; arbitrary number; grain errors; granular media coding; infinite family; t-grain-correcting codes; upper bounds; Entropy; Magnetic recording; Markov processes; Media; Probability distribution; Upper bound; Writing; Convex optimization; Gilbert–Varshamov bound; Markov chain; grain-correcting codes; granular media; lower bounds; magnetic recording; upper bounds;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2014.2301811
