PARALLEL DEMODULATION OF MULTIDIMENSIONAL SIGNALS

Imai and Hirakawa [17] and Ginzburg [16] have shown how algebraic codes of increasing Hamming distance can be combined with nested signal constellations of decreasing Euclidean distance to generate multidimensional signals with large distances. Cusack [8] and Savegh [21] have shown specific constructions of multidimensional constellations. Staged demodulation of these multidimensional constellations was suggested in [17]. With this procedure, the bits of the signal label protected by the most powerful code are decoded first, the bits protected by the second most powerful code are then decoded, and so on. This procedure is suboptimum, but reduced decoding complexity will result. In particular, staged decoding is amenable to an architecture with pipelined parallelism. In this paper, we consider the design of constellations that allow a high degree of parallelism in the staged decoder structure and in addition allow soft decoding of the component algebraic codes based on a systolic algorithm amenable to VLSI implementation. Combination of these multidimensional constellations with trellis-coded modulation (TCM) is also considered. Set partitioning is based on the partition of a linear code into a subcode and its cosets, and we show that a highly parallel demodulator structure can also be applied when TCM is used.