In this paper, we deal with convolutionally encoded MSK, DMSK and TFM signals. The matched convolutional encoding technique is used which was shown earlier to lead in some eases to the optimum Viterbi demodulation/decoder which is not more complex than the optimum receiver for the uncoded signal. Results of a systematic search for such cases are presented and discussed.>

A matched code is a convolutional code chosen in such a way that when combined with modulation with memory the resulting receiver for the coded modulation has the smallest possible number of states. In the paper, the matched coding technique is applied to coded tamed frequency modulation (TFM) schemes and a formal procedure is developed to find the best combination of a code and a modulation. The optimization criterion is the maximum free Euclidean distance for a given code rate and a given number of states in the Viterbi receiver used for the coded modulation. A search for the best codes was carried out for code rates 1/2 and 2/3, and for receivers with up to 256 and 64 states, respectively. Good coding gains (more than 7 dB for rate 1/2) were achieved. Some of the best codes were catastrophic, yet the coded modulation was not. The codes obtained using the matched coding approach were in many cases better than those obtained using traditional optimization techniques.>

The structure of combinations of (l,k) binary trellis encoders and fast frequency-shift keying (FFSK) modulation is studied. A novel method for the optimization of these combinations is proposed. It is concluded that, regardless of the particular realization, the best combinations can always be obtained by using a so-called matched convolutional code. Optimum FFSK codes of rates 1/2 and 2/3 for up to 64 and 32 states, respectively, are reported. It is shown that the best matched encoders for FFSK modulation are also matched and best for any FFSK-type scheme, where the pulse shape is required to satisfy Nyquist's third criterion.>