Description
A family of codes in permutations derived from \(q\)-ary linear codes, such as Lee-metric codes, RS codes [2], quadratic residue codes, and most binary codes.
Rate
Rank modulation codes with code distance of order \(d=\Theta(n^{1+\epsilon})\) for \(\epsilon\in[0,1]\) achieve a rate of \(1-\epsilon\) [3].
Realizations
Electronic devices where charges can either increase in an individual cell or decrease in a block of adjacent cells, e.g., flash memories [4].
Parent
Cousins
- Gray code — The rank-modulation Gray code is an extension of the original binary Gray code to a code on the permutation group [4].
- Linear \(q\)-ary code — Almost all linear \(q\)-ary codes can be converted to rank-modulation codes [2].
References
- [1]
- Anxiao Jiang, M. Schwartz, and J. Bruck, “Error-correcting codes for rank modulation”, 2008 IEEE International Symposium on Information Theory 1736 (2008) DOI
- [2]
- A. Mazumdar, A. Barg, and G. Zémor, “Constructions of Rank Modulation Codes”, (2011) arXiv:1110.2557
- [3]
- A. Barg and A. Mazumdar, “Codes in permutations and error correction for rank modulation”, 2010 IEEE International Symposium on Information Theory 854 (2010) DOI
- [4]
- Anxiao Jiang, R. Mateescu, M. Schwartz, and J. Bruck, “Rank Modulation for Flash Memories”, IEEE Transactions on Information Theory 55, 2659 (2009) DOI
Page edit log
- Victor V. Albert (2022-11-07) — most recent
- Victor V. Albert (2022-04-12)
- Jiaxin Huang (2022-04-08)
Cite as:
“Rank-modulation code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rank_modulation