A fast algorithm for uniform vector quantization

A design method for uniform vector codes and a fast processing implementation algorithm is presented for high-bit-rate high-quality data compression applications. The codes are designed as uniformly dirtributed and densely packed 2ⁿ-dimensional lattice points. First, the newly developed geometric approach to the 2ⁿ-dimensional lattice packing problem is presented. Codewords designed following the regular structure of a densely packed sublattice not only assume savings in dimensionality but are suitable for fast processing. The resulting codes in 4, 8, 16, and 32 dimensions are equivalent to those obtained from the corresponding known densest packed 4, 8, 16, and 32 dimensional lattices. This design algorithm uses pre-determined rules at the coder and decoder and requires no codeword storage. Compared to a full-search, this algorithm reduces the complexity of computation by approximately an exponential order of two. Its advantages relative to scalar codes are explored by comparing their rates and distortions.