  In this paper, rate adaptive coded Digital Phase Modulation (DPM) schemes
based on punctured ring convolutional codes are presented. We first present an
upper bound on symbol error probability for punctured convolutional coded
Continuous Phase Modulation (CPM) over rings with Maximum Likelihood Sequence
Detection (MLSD). The bound is based on the transfer function technique, which
is modified and generalized to punctured convolutional codes over rings. The
novelty of this paper is the development of the analytical upper bound on the
symbol error probability for the investigated system. This work provides a
systematic way to analyze and design the rate adaptive ring convolutional coded
CPM systems. The analysis method is very general. It may be applied to any
trellis based coding schemes.
