Mapping Design for General Multidimensional Communication Systems

Abstract In communication systems, the map-ping between the data space and the signal con-stellation needs to be carefully designed. The mapping based on the \Gray " code (or the Kar-naugh map) is a well known scheme for constella-tions with uniformly-distributed points. However, for some systems with an irregular constellation, like the permutation modulation system and the parallel combinatory DS/SS commnication system which, essentially, are multidimensional systems, the common method of mapping is invalid. In this paper, we propose a practical algorithm to nd a suboptimal mapping for a general constellation. For a constellation with M points, there are a to-tal of M! dierent mappings. To achieve computa-tional eciency, the algorithm is designed based on an incomplete search. A comparison of several mappings shows that very good mappings can be found by this systematic method.