The Design of Trellis Codes for Fading Channels

It has been well established in the literature that the appropriate criterion for optimum trellis coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. We show here that when trellis coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code for optimum performance is guided by other factors, in particular the lenffth of the shortest ereor event path, and the product of branch distances (Possibly normalized by the Euclidean distance of the path) along that Path. Although maximum free distance (dfree) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure for optimization of trellis codes transmitted over Rician fading channels. If no interleavingldeinterleaving is used, then once again the design of the trellis code is guided by maximizing dfree. It is also shown that allowing for multiple symbols per trellis branch, i.e., multiple trellis coded modulation (WTCM), provides an additional degree of freedom for designing a code to meet the above optimization criteria on the fading channel. potential. It is here where the MTCM technique exploits its f u l l