Coset Partitioning Construction of Systematic Permutation Codes Under the Chebyshev Metric

Abstract

The rank-modulation scheme has been recently proposed to write and store data in flash memories efficiently. In this paper, a new construction of systematic error-correcting codes for permutations is presented under the Chebyshev distance. By constructing a subgroup code and using its coset codes to partition the set of information permutations, the proposed code construction can achieve much larger code cardinality and hence higher code rates. To facilitate the encoding and decoding of the constructed codes, we also investigate the concepts of ranking and unranking for permutations, and generalize them to $M$ -ranking and $M$ -unranking for multi-permutations. Examples are provided to demonstrate the relevant concepts and the encoding/decoding algorithms.