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New Bounds and Constructions for Granular Media Coding.
- Source :
-
IEEE Transactions on Information Theory . Aug2015, Vol. 61 Issue 8, p4227-4238. 12p. - Publication Year :
- 2015
-
Abstract
- Improved lower and upper bounds on the size and the rate of grain-correcting codes are presented. The lower bound is Gilbert–Varshamov-like combined with a construction by Gabrys et al., and it improves on the previously best known lower bounds on the asymptotic rate of \lceil \tau n \rceil -grain-correcting codes of length n on the interval [0,0.0668] . One of the two newly presented upper bounds improves on the best known upper bounds on the asymptotic rate of \lceil \tau n \rceil -grain-correcting codes of length n on the interval \tau \in (0,{1}/{8}] and meets the lower bound of {1}/{2} for \tau \geq 1/8 . Moreover, in a nonasymptotic regime, both upper bounds improve on the previously best known results on the largest size of t -grain-correcting codes of length $n$ , for certain values of n$ and t$ . Constructions of 1-grain-correcting codes based on a partitioning technique are presented for lengths up to 18. Finally, a lower bound of on the minimum redundancy of $\infty $ -grain-detecting codes of length $n$ is presented. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 61
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 108358205
- Full Text :
- https://doi.org/10.1109/TIT.2015.2445758