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We present a new method, called Voronoi extension, for the design of low-complexity multi-rate lattice vector quantization (VQ). With this technique, lattice codebooks of arbitrarily large bit rates can be generated algorithmically and the problem of lattice codebook overload can be bypassed. We describe a practical multi-rate quantization system based on Voronoi extension and derived from the lattice RE8. This system is applied to the TCX coding model using pitch prediction, so as to extend AMR-WB speech coding at high bit rates (in particular 32 kbit/s).