| CPM modulators can be decomposed into a recursive encoder followed by a memoryless mapper. For modulation indices of the form $h=K/P$ with odd $K$, the encoder generates a time-varying phase trellis with $2PM^{L-1}$ states, where $L$ is the number of symbol taps in the premodulation filter. For symmetric and analytically tractable premodulation filters like in the case of GMSK, this time-varying trellis can be very efficiently implemented in VLSI allowing for very low storage requirements and high data rates at the output of the digital circuit. This paper demonstrates how the transfer function matrix of such a time-varying trellis can be modified to precode the data bits to eliminate double errors and/or allow for an encoder state independent trellis termination. This paper further proves that a $PM^{L-1}$ state MAP decoder is optimum for this time-varying trellis. Thus, employing a time-varying CPM trellis at the transmitter allows for simplified modulator structures without increasing the receiver complexity. |