On the Combination ofMultilevel Coding and Signal

| In this paper, the combination of signal shaping and coding in mul-tilevel coding schemes is discussed. It is shown that for optimized discrete Gaus-sian distributed signal points the gap to the Shannon limit is negligible. Since for nite constellations coding and shaping are not separable, the optimum sharing of the total redundancy between coding and shaping is derived. It turns out that for combined coding and shaping 1 bit redundancy per dimension is necessary to achieve optimum performance. Furthermore, the optimal rate assignment in a multilevel coding scheme when shaping is active is presented. In practice, noticeable shaping gains are only achievable if the presented rules are taken into account. Simulation results show that, for an optimized shaping redundancy and optimum rate design, multile-vel coding with large block length achieves BER = 10 ?5 exactly at the capacity limit for equiprobable signal points.