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.
| Original language | English |
|---|---|
| Pages (from-to) | 3685-3695 |
| Number of pages | 11 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 52 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Aug 2006 |
Keywords
- Code constructions
- Distance bounds
- Distance-preserving mappings (DPMs)
- Hamming distance
- Permutation coding
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences