Address Decomposition for the Shaping of Multi-dimensional Signal Constellations

In this work, we introduce an efficient addressing scheme to realize points near to the knee of the tradeoff curves of an optimally shaped constellation. This scheme, called as the address decomposition, is based on decomposing the addressing into a hierarchy of the addressing steps each of a low dimensionality. As the memory size associated with a direct addressing scheme has an exponential growth with the dimensionality, this decomposition of the addressing results in a substantial decrease in the complexity. In this case, by using a memory of a practical size, we can move along a tradeoff curve which is nearly optimum. For example, in a space of dimensionality N = 32, we use a block of memory of 2.5 kilo-bytes per N dimensions to achieve a shape gain of y, = 0.92 dB with CER, = 1.25, PAR = 2.95. This scheme has no associated computation, is straightforward to implement and is adaptable to the structure of a general coset coding scheme