Title :
A Generalized Upper Bound and a Multilevel Construction for Distance-Preserving Mappings
Author :
Swart, Theo G. ; Ferreira, Hendrik C.
Author_Institution :
Electr. & Electron. Eng. Sci., Univ. of Johannesburg
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
Keywords :
Hamming codes; binary sequences; DPM; Hamming distance; binary sequence; distance-increasing mapping; distance-preserving mapping; distance-reducing mapping; multilevel construction; permutation sequence; Africa; Australia; Binary sequences; Block codes; Convolutional codes; Error correction codes; Hamming distance; Information theory; Upper bound; Code constructions; Hamming distance; distance bounds; distance-preserving mappings (DPMs); permutation coding;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2006.878175
