How to design an efficient lattice coding scheme

Lattice codes find applications in various digital communications settings, including shaping for power-constrained channels, coding with side information (dirty-paper channel, Wyner-Ziv source), and Gaussian networks. In this paper we deal neither with the construction of a good lattice, nor with algorithms for lattice coding and decoding, but with other elements of a lattice coding system. We shall consider (1) the two roles of the fundamental cell of the shaping lattice; (2) efficient mappings from information bits to a lattice point; (3) the loss due to a finite alphabet in construction-A lattices; (4) randomization with a simple dither; and (5) how to incorporate a multi-dimensional lattice into a sequential (feedback) scheme. While these are not new issues and observations, they seem to be somewhat overlooked or hidden inside the rich literature about lattice codes.