Optimization of trellis coded TFM via matched codes

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.<>