Fast lexicographical order-based encoder for lattice vector quantization of Generalized Gaussian sources using pre-computed n-balls cardinalities

A fast indexing method dedicated to lattice vector quantization (LVQ), called stack indexing (SI), is presented. It is based on the approach previously proposed by Loyer et al. (2003). Our method addresses the problem of enumerating codebook vectors in lattice Zn and is designed for the compression of Generalized Gaussian sources. Indexing is the key point of the lossless stage of LVQ. It usually requires a high number of additions and thus is often critical in terms of execution time. To circumvent this drawback, SI uses pre-computed cardinalities of n-balls in Zn to enumerate lattice vectors in the lexicographical order. The algorithmic complexity of the SI is low and the number of additions performed does not depend on the dynamic range of the source which makes SI well suited for high dynamic sources. Experimental results performed in still image coding using a discrete wavelet transform confirm that the computational cost is significantly decreased compared to the previous approach.