Mapping design for general multidimensional communication systems

In communication systems, the mapping between the data space and the signal constellation needs to be carefully designed. The mapping based on the “Gray” code (or the Karnaugh map) is a well known scheme for constellations with uniformly-distributed points. However, for some systems with an irregular constellation, like the permutation modulation system and the parallel combinatory DS/SS communication system which, essentially, are multidimensional systems, the common method of mapping is invalid. In this paper, we propose a practical algorithm to find a suboptimal mapping for a general constellation. For a constellation with M points, there are a total of M! different mappings. To achieve computational efficiency, 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