Storage efficient decoding for a class of binary be Bruijn sequences Original Research Article

A binary span k de Bruijn sequence is a binary sequence of period 2k such that each k-tuple of bits occurs exactly once as a subsequence in a period of the sequence. The de Bruijn sequences have applications in position sensing and range finding, as well as in other areas, by virtue of this subsequence property. To make use of a particular de Bruijn sequence, we need to be able to determine the position of an arbitrary k-tuple in the sequence. We refer to this as ‘decoding’ the sequence. In this paper we use the structure of a class of de Bruijn sequences, originally constructed by Lempel, to give an algorithm for decoding that is fast, yet more space efficient than a complete look-up table of subsequences and their positions in a sequence. We also consider the case where the displacement between consecutive subsequences whose positions are decoded is restricted and obtain a further marked improvement in storage.