Trellis coded CPFSK over rings

The paper presents ring trellis coded CPFSK in which the encoder has the same algebraic structure as the memory part of the CPM modulator. For M-ary CPFSK with a modulation index h=1/M, the authors show that this approach leads to a natural combination of the convolutional encoder with the memory part of the modulator. After a general presentation of trellis coding over the ring of integers of CPFSK, they examine quaternary and octonary modulations and compare them to previously proposed schemes. The results demonstrate the superiority of ring trellis coded CPFSK over conventional convolutionally encoded CPFSK.