Window Weight Limited Gray Codes and Robust Positioning Sequences

Window Weight Limited (WWL) strings and codes have been studied recently owing to their various applications, including DNA based storage and energy-harvesting. In this work, we proposed to study a new coding scheme, called WWL Gray code. This is a list of WWL strings in Gray order, that is, the Hamming distance of two consecutive strings in the list is one. We are the first to investigate the WWL Gray codes with efficient rankinglunranking algorithms. We show that the WWL Gray codes are useful in designing robust positioning sequences. Note that the robust positioning sequences have attracted a lot of attentions recently owing to their numerous applications, including quantum communications and robot localization. In this work, using the WWL Gray codes, we obtain robust positioning sequences with less redundancy compared to the best known results.