Lattice labeling algorithms for vector quantization

Labeling algorithms for construction-A and construction-B lattices with respect to pyramid boundaries are presented. The algorithms are developed based on relations between lattices and linear block codes as well as on transformations among several specifically defined lattices and their translations. The mechanism for the construction of these algorithms can be considered as an extension of that given by Fischer (1986). The algorithms are noted to achieve 100% efficiency in utilizing index bits for binary representations. Furthermore, it is determined that many important lattices (E₈, Λ₁₆...) can be indexed to arbitrary norms and dimensions. The complexity of these algorithms in terms of both memory and computation is quite low and thus it is possible to develop practical lattice vector quantizers of large norms and high dimensions using these algorithms