Design of entropy-constrained quantizers based on coset codes

Asymptotic vector quantization (VQ) theory indicates that at high rates, the optimal VQ uniformly places its reproduction vectors in the high dimensional space in a manner that each of the quantization cells is made as spherical as possible. As compared with scalar quantizers whose quantization cells are cubic, VQ exploits the space-filling efficiency of its constituent convex polytope and hence achieves the so-called granular gain.<>