Codificação analógica via projeções de reticulados

In this paper we study a class of codes for the transmission of a discrete-time continuous alphabet source over a Gaussian channel. Our proposal differs from the ones found in the literature, that mostly deal with one dimensional continuous sources, in the sense that the scheme proposed here encodes sources with k-dimensional support to be transmitted over n-dimensional channels in the bandwidth expansion regime (n > k). The codes considered are associated to a piecewise continuous application. We describe the geometry of such codes, highlighting their connection with the search for good families of projections of the cubic lattice Zn. From this relation, we design an efficient decoding algorithm and exhibit some explicit construction with good simulation performance.