A device for transmitting information in a communications signal is envisioned. The information is modulated, at least in part, with a first angle-related characteristic. The device has a digital conversion circuit operable to convert information to be broadcast into a digital form. A constellation mapper is coupled to the digital conversion circuit, and is operable to convert the digital information into information associated with a constellation. A trajectory generation circuit generates samples denoting a trajectory within the constellation for the information. A transition analysis circuit determines a change in value of an angle-related characteristic in a transition between two samples, and a threshold detection circuit detects whether the change in value fails to meet a particular threshold. An angle-related characteristic distribution circuit can then distribute a portion of the change in value associated with the transition to at least one other transition.