Golomb Ruler Research Articles

Acquisition sequences in PPM communications (Corresp.)

In pulse position modulation (PPM) communications an acquisition sequence is needed to establish frame synchronization for subsequent data transmission. This sequence must have PPM structure (one pulse per frame) and desirable autocorrelation properties for its detection. The problem of finding aperiodic PPM acquisition sequences having the minimum possible autocorrelation for all off-shifted positions is investigated. Sequences with the maximum possible number of frames have been found up to frame size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15</tex> . Examples are given for every frame length up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">88</tex> , and powers of two up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1024</tex> . An interesting relation between the PPM sequence problem, Costas and sonar arrays, and Golomb's ruler is explored.

Addendum to "Optimum Golomb Rulers"

The optimum Golomb ruler1 with 13 marks has been found. This shortest ruler as well as another new ruler is reported.

Optimum Golomb Rulers

A Golomb ruler has m division marks with the spacings between marks positive integers such that the set of (m2 − m)/2 measurements which can be made between the marks are distinct. A fast search procedure is outlined for determining the shortest ruler. For 12 marks the shortest ruler is 85 units.