Multiple symbol differentially detected multilevel codes for the Rayleigh-fading channel

Conventional differential detection is known to perform poorly on the fast-fading Rayleigh-fading channel due to the rapid variation of the channel state. The technique of multiple symbol differential detection (MSDD) improves the error performance by detecting over a sequence of symbols and exploiting the inherent correlation of the fading process. To further reduce the error rate, we need to introduce some form of coding. Successful coding for the Rayleigh-fading channel requires interleaving to decorrelate the channel-a conflicting requirement to MSDD. We propose a solution consisting of interleaving blocks of L M-ary phase-shift keying (MPSK) symbols that are multiple symbol differentially detected. The blocks are treated as elements of an M^L symbol alphabet over which a multilevel code based on geometrically uniform partitions is defined