Combined modulation and coding for continuous-phase FSK with nonuniform alphabet

The problem of combined coding and modulation is addressed for M-ary continuous-phase frequency-shift-keying (CPFSK) with a redundant symbol alphabet. It is shown that in many cases of interest, the use of a nonuniform mapping between coded bits and phase increments at the CPFSK modulator allows for a significant increase of free Euclidean distance in the coder/modulator state trellis as compared to the uniform alphabet case. A systematic search for optimum encoder/mapper/modulator structures is carried out for short constraint length rate 1/2 and 2/3 codes combined with 4-ary and 8-ary CPFSK, respectively, and for a relevant set of rational modulation indexes. The power-bandwidth efficiency of the optimum schemes is discussed and compared with that exhibited by the best coder/modulator structures previously proposed in the literature