A systematic approach to the construction of bandwidth-efficient multidimensional trellis codes

We present a unified approach to the construction of multidimensional trellis codes that have small constellation expansion ratio (CER) and small peak-to-average power ratio (PAR) and hence are of high bandwidth efficiency. In the approach, we extend Wei's (1987) construction to dimensionalities other than a power of two and propose a low-complexity encoder. We also present a general partition technique that gives geometrically uniform partitions with a good distance profile. The proposed method can generate many good codes including previously reported Ungerboeck codes, Gallager-Calderbank-Sloane codes, and Wei codes with quadrature amplitude modulation signals. Some newly discovered six-dimensional trellis codes are compared with these known codes on their CER, PAR, effective coding gain, and encoder/decoder complexities.