New-distance-metric based MLC in the presence of fading

A new distance metric is proposed to design optimal multilevel codes/parallel decoding of levels (MLC/PDL) system. Combining the constellation's intra-subset and inter-subset distances jointly, the metric describes not only the difference between the points in the same subset, but also the difference between the subsets that include the corresponding points. The metric reflects the real distinction in the points. The validity of the metric is proven through a series of simulations including 8PSK with Ungerboeck (1982) partitioning (UP) and block partitioning (BP), respectively. On the basis of the metric, we design an MLC/PDL system with surprising reliability, short time delay and decoding complexity.