Detection of a class of coded and phase-modulated signals

A system transmits data as phase-modulated signals over a noisy channel. In each of subintervals the carrier phase has one of possible values where is a prime number. The first phase coordinates are specified by the information source while the other coordinates are derived through a linear coding scheme in a polynomial field of elements. The receiver contains a phase detector and a decoder that operates algebraically on quantized phase values using a polynomial representation. It explores the fact that a correctable error must contain at least one member of a small set of error polynomials. The probability of a decoding failure and the required amount of computation is studied in detail when . The average amount of computation is small for codes of moderate length but at a certain critical length it starts to increase exponentially. Numerical results on the probability of a detection failure is available when and for . They show a degradation in SNR of more than dB compared to an ideal detector.