Estimating the distortion and entropy-coded bit rate of lattice vector quantiser for a Laplacian source

For practical use of lattice vector quantisers (LVQs), the codebook sizes are pre-decided and the lattice is scaled to control quantisation distortion and bit rate. Formulas are derived, estimating both the distortion and the bit rate as functions of a scaling factor of a LVQ, while a lossless coding method is specified as the rotational coordinate method and input sources are assumed to be Laplacian sources. Unlike conventional approaches based on asymptotical assumptions, the codebook size is limited first, and then the vector space is partitioned according to the characteristic of the source distribution. The proposed estimates are more realistic for practical applications because they handle practical codebook sizes. The lattice points are also counted at each surface on which lattice points exist. The Monte Carlo simulation verifies that the proposed estimates are accurate enough for determining the optimal scaling factor