TY - GEN

T1 - On the labeling problem of permutation group codes under the infinity metric

AU - Tamo, Itzhak

AU - Schwartz, Moshe

PY - 2011

Y1 - 2011

N2 - Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which produces an isomorphic code, may drastically change the minimal distance of the code. Thus, we may choose a code structure for efficient encoding/decoding procedures, and then optimize the code's minimal distance via relabeling. We formally define the relabeling problem, and show that all codes may be relabeled to get a minimal distance at most 2. The decision problem of whether a code may be relabeled to distance 1 is shown to be NP-complete, and calculating the best achievable minimal distance after relabeling is proved hard to approximate. Finally, we consider general bounds on the relabeling problem. We specifically show the optimal relabeling distance of cyclic groups. A specific case of a general probabilistic argument is used to show AGL(p) may be relabeled to a minimal distance of p -O(√pIn)

AB - Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which produces an isomorphic code, may drastically change the minimal distance of the code. Thus, we may choose a code structure for efficient encoding/decoding procedures, and then optimize the code's minimal distance via relabeling. We formally define the relabeling problem, and show that all codes may be relabeled to get a minimal distance at most 2. The decision problem of whether a code may be relabeled to distance 1 is shown to be NP-complete, and calculating the best achievable minimal distance after relabeling is proved hard to approximate. Finally, we consider general bounds on the relabeling problem. We specifically show the optimal relabeling distance of cyclic groups. A specific case of a general probabilistic argument is used to show AGL(p) may be relabeled to a minimal distance of p -O(√pIn)

UR - http://www.scopus.com/inward/record.url?scp=80054814389&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6034263

DO - 10.1109/ISIT.2011.6034263

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AN - SCOPUS:80054814389

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 879

EP - 883

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

Y2 - 31 July 2011 through 5 August 2011

ER -