A Survey of Combinatorial Gray Codes
SIAM Review
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Permutation Generation Methods
ACM Computing Surveys (CSUR)
Ranking and unranking permutations in linear time
Information Processing Letters
Linear-time ranking of permutations
ESA'07 Proceedings of the 15th annual European conference on Algorithms
A dynamic programming algorithm for constructing optimal prefix-free codes with unequal letter costs
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Optimal Prefix Codes for Infinite Alphabets With Nonlinear Costs
IEEE Transactions on Information Theory
Data movement in flash memories
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Correcting charge-constrained errors in the rank-modulation scheme
IEEE Transactions on Information Theory
Correcting limited-magnitude errors in the rank-modulation scheme
IEEE Transactions on Information Theory
Rewriting codes for joint information storage in flash memories
IEEE Transactions on Information Theory
Zombie memory: extending memory lifetime by reviving dead blocks
Proceedings of the 40th Annual International Symposium on Computer Architecture
Hi-index | 755.02 |
We explore a novel data representation scheme for multilevel flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The only allowed charge-placement mechanism is a "push-to-the-top" operation, which takes a single cell of the set and makes it the top-charged cell. The resulting scheme eliminates the need for discrete cell levels, as well as overshoot errors, when programming cells. We present unrestricted Gray codes spanning all possible n-cell states and using only "push-to-the-top" operations, and also construct balanced Gray codes. One important application of the Gray codes is the realization of logic multilevel cells, which is useful in conventional storage solutions. We also investigate rewriting schemes for random data modification. We present both an optimal scheme for the worst case rewrite performance and an approximation scheme for the average-case rewrite performance.