Upper bound of single-track Gray codes and the combined coding method of period 2ⁿ

Abstract

Single-track Gray code is a special class of Gray codes that all the columns of its codewords are shifted equivalent. The upper bound of single-track Gray codes is discussed on necklace orderings and self dual necklace orderings. As no length n period 2n single track Gray code exists, extra reading heads are inevitable to obtain period 2n code and in the worst situation 2n reading heads may have to be used. To solve this problem, a subdivision code is defined. Combining a single-track Gray code and the subdivision code, a double-track Gray code can be constructed that have period zn and may reduce the number of reading heads. In that worst 2n reading heads situation, only n+ 1 reading heads are adequate when use combined absolute coding method to obtain period zn.

Novel Absolute Rotary Position Sensor Based on Combination of Gray Scale Pattern Disc

“…Optical rotary sensor classically have a binary code disc based on the gray code in which there is only a single bit changing during a transition from one position to the next to minimize readout errors due to non-ideal transitions. Many improvements of the gray code based pattern is reported [12][13][14][15]. Digital absolute rotary sensors which are not only accurate, light, small, and insensitive to EM interference but also characterized by their high resolution are reported, however, in these sensors, the encoder design is complex and contains numerous parts such as several light sources or an array of photo-detectors in the detection scheme [16][17][18][19][20].…”

A Novel Approach of an Absolute Encoder Coding Pattern

“…However, to encode 2 n positions, n separate tracks and sensor channels are needed. Many improvements of the Gray code based pattern have been published in recent years [1]- [4]. There also exist absolute encoders based on De Bruijn [5] sequences or pseudorandom code patterns [6], [7], which consist of only a single track used to find the position.…”