Higher-order terms in asymptotic expansion for information loss in quantized random processes

Uniform quantization of random vectors onto ε-grids εZⁿ is considered. Higher-order terms in asymptotic expansions for the entropy of the ε-quantized random vector and for the loss of the mutual information between two random vectors under such quantization as ε → 0+ are obtained. The coefficients in these asymptotics are explicitly calculated for Gaussian distributed vectors. Taken for initial segments of stationary Gaussian sequences, these factors have limit average values per unit of time. For such sequences governed by state-space equations, computation of these average values is reduced to solutions of algebraic matrix Riccati and Lyapunov equations.