A Generalized Upper Bound and a Multilevel Construction for Distance-Preserving Mappings

Authors:
T. G. Swart;H. C. Ferreira
Affiliations:
Electr. & Electron. Eng. Sci., Univ. of Johannesburg;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

A new general upper bound is derived on the sum of the Hamming distances between sequences when mapping from one set of sequences to another. It is shown that a similar upper bound for mappings from binary sequences to permutation sequences is a special case of this upper bound and this is used to evaluate known mappings. Also, new distance-preserving mappings (DPMs) from binary sequences to permutation sequences are presented, based on a multilevel construction. In addition to explicit distance-conserving mappings, distance-increasing, and distance-reducing mappings are also presented. Several of the new DPMs attain the upper bound