Abstract:
A system transmits data as phase-modulated signals over a noisy channel. In each ofrsubintervals the carrier phase has one ofppossible values wherepis a prime number. The...Show MoreMetadata
Abstract:
A system transmits data as phase-modulated signals over a noisy channel. In each ofrsubintervals the carrier phase has one ofppossible values wherepis a prime number. The firstkphase coordinates are specified by the information source while the otherr-kcoordinates are derived through a linear coding scheme in a polynomial field ofM = p^{k}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 whenp = 3. 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 whenp = 3and5forM < 1000. They show a degradation in SNR of more than3dB compared to an ideal detector.
Published in: IEEE Transactions on Information Theory ( Volume: 12, Issue: 2, April 1966)