A class of codes for polyphase signals on a bandlimited Gaussian channel

A new class of codes is defined and analyzed when applied to a communication system that sends data over a bandlimited Gaussian channel. A code word is defined as a sequence of -phase values and transmitted either modulated on a carrier or transformed into samples on a baseband channel. An algebraic procedure is used to generate the phase sequence from a set of equidistant angles. The baseband model is analyzed in detail and the performance is evaluated by first assuming an ideal detector and computing an error-probability bound. Taking , and , codes are shown to exist that perform close to the theoretical limit. The algebraic structure of these codes much simplifies the numerical analysis. A second receiver is defined that extracts phase values out of the received waveform and then performs a suitable quantization. The degradation of this detector appears to be moderate for low information rates when evaluated for . A carrier phase-modulated system is also defined and evaluated with a performance quite similar to the baseband model.