Lattice shell codes and constant energy codes

Abstract

It was found that minimum Hamming distance between code sequences can be increased using a generalised coset code combined with block code partitioning of a lattice. The performance of these codes improves as dimensionality increases. Simulation results show good performance for generalised coset codes in the Rayleigh fading channel under two important assumptions. First, the availability of CSI at the receiver and second, that infinite interleaving were assumed. Without these assumptions the decoding algorithms would perform very poorly. In this paper we discuss another class of Euclidean space code called shell codes or constant energy codes. This type of code has the interesting property that the sum of energies over a fixed number of symbols, the dimensionality of the signal constellation, equates to a constant value. Using the constant energy of these types of code a different decoding algorithm can be applied. This eliminates the use of a Euclidean distance metric, while requiring only partial CSI and no interleaving. There are two different types of multidimensional signal constellations that have constant energy. The first is derived from a lattice shell and the second are those derived from sequences of constant energy 2 dimensional constellations such as PSK. © 2011 IEEE.