Efficient, nearly optimum addressing schemes based on partitioning the constellation into the union of blocks

Abstract

'Abstract: In this paper, we introduce two efficient addressing schemes for the nearly optimum shaping of multi-dimensional signal spaces. Using K concentric circles, the 2-D (two-dimensional) subspaces are partitioned into K shells of equal volume. is to find a one-to-one mapping between the set of these n-tuples and the set of the integers (0, T -1 1 such that the mapping and its inverse can be easily implemented. In the proposed schemes, the N-D clusters are grouped into blocks such that the addressing within the blocks, which is achieved using a common algorithm for all the blocks, has a low complexity. The addressing of the blocks is based on some recursive relationship which allows us to decompose the problem into smaller parts each of a low complexity. The overall scheme requires a moderate amount of memory and has a small computational complexity. The introduced methods are compared with the previously known schemes. The reduction in the complexity is substantial.