Lattice-based designs of direct sum codebooks for vector quantization

A direct sum codebook (DSC) has the potential to reduce both memory and computational costs of vector quantization. A DSC consists of several sets or stages of vectors. An equivalent code vector is made from the direct sum of one vector from each stage. Lattice based DSC quantizers are designed to be optimal under a residual encoding by avoiding entanglement. Experimental results show that DSC quantizers based on cubical lattices perform as well as exhaustive search quantizers on a scalar source. Performance increases with vector dimension on sources with memory, though not quite as much as with an exhaustive search. Additional savings in rate are obtainable by using variable length code vectors.