For a general class of constant-energy trellis-coded modulation (TCM) schemes with 2/sup /spl nu// states, necessary and sufficient conditions to guarantee that a maximum-likelihood sequence estimator (MSLE) can decode each symbol with a fixed delay of /spl nu/ symbols are derived. Additive white Gaussian noise (AWGN) is assumed. Minimum shift keying (MSK) is a special case that belongs to the family of modulation schemes with /spl nu/=1. It is shown that when these conditions are met, the minimum squared Euclidean distance is upper-bounded by 4E/sub s/, where E/sub s/ is the signal's energy per interval. Necessary and sufficient conditions to achieve the upper bound are given and it is shown that these conditions are met if and only if the TCM scheme can be implemented as pulse amplitude modulation (PAM) using a pulse that extends over /spl nu/+1 symbols. Signals that achieve this upper bound and maximize the power within a given bandwidth are found. The bandwidth efficiency of such schemes is significantly higher than that of MSK.

Rate 1/2 convolutional codes over the ring of integers modulo M are combined with M-ary continuous phase modulation (CPM) schemes whose modulation indices are of the form h=1/M. An M-ary CPM scheme with h=1/M can be modeled by a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is linear over the ring of integers modulo M. The fact that the convolutional code and the CPE are over the same algebra allows the state of the CPE to be fed back and used by the convolutional encoder. A modified Euclidean distance function that substantially simplifies the search for good codes has been derived and used to find new codes. Numerical results show that this approach consistently improves the performance as compared to coded schemes using binary convolutional codes with the same decoding complexity.

Continuous phase modulation (CPM) schemes are bandwidth and energy efficient constant-envelope modulation schemes that can be viewed as a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is of convolutional type. It is observed that CPM schemes can be catastrophic in the sense that pairs of input sequences that differ in an infinite number of positions can be mapped into pairs of signals with finite Euclidean distance. This can happen in spite of the fact that the CPE is never catastrophic when considered as a stand alone convolutional encoder. The necessary and sufficient condition for a general CPM scheme to be catastrophic is given. Each member of the two major families of CPM schemes, namely the LREC and the LRC, has been classified as a catastrophic or noncatastrophic scheme. For the catastrophic schemes, the probability that a catastrophic event occurs is determined. A canonical precoder which transforms each scheme of both families into an equivalent noncatastrophic scheme is derived. The equivalent noncatastrophic scheme has the same number of states as the original one. Moreover, it has the property that if two input sequences differ in the ith position, the corresponding output signals have nonzero Euclidean distance in the ith interval.>