Adjacency-hopping de Bruijn Sequences for Non-repetitive Coding
Bin Chen Zhenglin Liang Shiqian Wu
A special type of cyclic sequences named adjacency-hopping de Bruijn
sequences is introduced in this paper. It is theoretically proved the existence
of such sequences, and the number of such sequences is derived. These sequences
guarantee that all neighboring codes are different while retaining the
uniqueness of subsequences, which is a significant characteristic of original
de Bruijn sequences in coding and matching. At last, the adjacency-hopping de
Bruijn sequences are applied to structured light coding, and a color fringe
pattern coded by such a sequence is presented. In summary, the proposed
sequences demonstrate significant advantages in structured light coding by
virtue of the uniqueness of subsequences and the adjacency-hopping
characteristic, and show potential for extension to other fields with similar
requirements of non-repetitive coding and efficient matching.