The root lattices as low bit rate vector quantizers

Vector quantizers based on the A and D lattices are explored, using the mean square error (MSE) fidelity criterion for independent identically distributed sources with normal, Laplacian, and gamma probability density functions. Code books are studied for uniform coding rates of up to 2 b/sample and two and four dimensions. The expected MSE performance of the quantizers is better than that of optimal (nonuniform) Lloyd-Max quantizers. While the design algorithm presented offers only modest improvements in MSE performance for a normally distributed source, improvement gains of up to several decibels can be achieved when coding Laplacian and gamma sources