Set partitioning for multilevel codes on a Rayleigh-fading channel

On a Rayleigh-fading channel, multilevel codes achieve larger Hamming distances than single-level codes at comparable decoder complexity and bandwidth efficiency by employing a multistage decoder. Typically, multilevel codes are designed using Ungerboeck's (1982) set partitioning. This results in a large path multiplicity that degrades the code performance significantly. In order to overcome the performance degradation, we propose a set partitioning method that greatly reduces the path multiplicity.