Asymptotically Optimal Fixed-Rate Lattice Quantization for a Class of Generalized Gaussian Sources

Asymptotic expressions for the optimal scaling factor and resulting minimum distortion , as a function of codebook size N, are found for xed-rate k-dimensional lattice vector quantization of generalized Gaussian sources with decay parameter 1. These expressions are derived by minimizing upper and lower bounds to distortion. It is shown that the optimal scaling factor a N decreases as (lnN) 1== N ?1=k and that for scale-optimized lattice quantization, granular distortion asymptotically dominates overload distortion. Consequently, the minimum distortion is D N = c (ln N) 2== N ?2=k. This result indicates that the distortion of optimal lattice quantizers diverges from that of asymptotically optimal vector quantization, as N increases.