Combined concatenated coding and modulation schemes using a redundant signal alphabet

Combined concatenated coding and modulation schemes using redundant signal alphabets are presented. A 2^m+1-point signal constellation is employed to transmit m information bits per symbol (as in Ungerboeck schemes). To avoid a loss in spectral efficiency, the available redundancy (1 b/symbol duration) is shared between an outer error-correcting code and an inner code combined with a multidimensional modulation. The analytical performance of the schemes presented is evaluated on an additive white Gaussian noise (AWGN) channel. Simulation results indicate that 8 dB of coding gain at a bit error rate of 10^-11 can be obtained with simple concatenated codes having a spectral efficiency of 3 b/s/Hz, thus achieving a better performance/complexity tradeoff than Ungerboeck codes