On the Capacity of Constrained Permutation Codes for Rank Modulation

Sarit Buzaglo; Eitan Yaakobi

doi:10.1109/tit.2016.2519400

On the Capacity of Constrained Permutation Codes for Rank Modulation

IEEE Transactions on Information Theory ◽

10.1109/tit.2016.2519400 ◽

2016 ◽

Vol 62 (4) ◽

pp. 1649-1666 ◽

Cited By ~ 3

Author(s):

Sarit Buzaglo ◽

Eitan Yaakobi

Keyword(s):

Permutation Codes ◽

Rank Modulation

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Partial rank modulation for flash memories

2010 IEEE International Symposium on Information Theory ◽

10.1109/isit.2010.5513597 ◽

2010 ◽

Cited By ~ 13

Author(s):

Zhiying Wang ◽

Jehoshua Bruck

Keyword(s):

Flash Memories ◽

Rank Modulation

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A Message-passing Algorithm Realizing MAP Decoding of Kløve’s Permutation Codes

2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing (ISTC) ◽

10.1109/istc.2018.8625268 ◽

2018 ◽

Author(s):

Motohiro Kawasumi ◽

Kenta Kasai

Keyword(s):

Message Passing ◽

Permutation Codes ◽

Message Passing Algorithm ◽

Map Decoding

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Re-synchronization of permutation codes with Viterbi-like decoding

2009 IEEE International Symposium on Power Line Communications and Its Applications ◽

10.1109/isplc.2009.4913400 ◽

2009 ◽

Cited By ~ 6

Author(s):

Ling Cheng ◽

Theo G. Swart ◽

Hendrik C. Ferreira

Keyword(s):

Permutation Codes

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A Bound on Permutation Codes

The Electronic Journal of Combinatorics ◽

10.37236/2929 ◽

2013 ◽

Vol 20 (3) ◽

Cited By ~ 2

Author(s):

Jürgen Bierbrauer ◽

Klaus Metsch

Keyword(s):

Projective Plane ◽

Symmetric Group ◽

Minimum Distance ◽

Main Part ◽

Latin Squares ◽

Permutation Codes ◽

Permutation Code ◽

Mutually Orthogonal Latin Squares ◽

Hamming Metric ◽

Completion Theorem

Consider the symmetric group $S_n$ with the Hamming metric. A permutation code on $n$ symbols is a subset $C\subseteq S_n.$ If $C$ has minimum distance $\geq n-1,$ then $\vert C\vert\leq n^2-n.$ Equality can be reached if and only if a projective plane of order $n$ exists. Call $C$ embeddable if it is contained in a permutation code of minimum distance $n-1$ and cardinality $n^2-n.$ Let $\delta =\delta (C)=n^2-n-\vert C\vert$ be the deficiency of the permutation code $C\subseteq S_n$ of minimum distance $\geq n-1.$We prove that $C$ is embeddable if either $\delta\leq 2$ or if $(\delta^2-1)(\delta +1)^2<27(n+2)/16.$ The main part of the proof is an adaptation of the method used to obtain the famous Bruck completion theorem for mutually orthogonal latin squares.

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