Multilevel-codes: Distance Prooles and Channel Capacity

The calculation of the average proole of the squared Euclidean distance is derived for the individual coding levels of multilevel-coding schemes using the weight e n umerators of the binary linear component codes. It is shown that the multiple representation of binary symbols at low coding levels causes a signiicant loss in power eeciency. This eeect can also be observed for the capacities of the equivalent c hannels at the individual coding levels, which are derived. It is proven that the capacity o f a n y digital modulation scheme can be achieved by a m ultilevel-coding scheme together with multistage-decoding in principle. The results allows an optimum tuning of the rates for the component codes. Die Ergebnisse erlau-ben eine optimale Aufteilung der Rate auf die einzelnen Komponentencodes.