RD Optimization of uniform threshold scalar quantization for Laplacian distributions

Following many papers [1], [2], [3] and references therein, we address the problem of the optimal quantization. The Rate-Distortion Optimization (RDO) of the dead-zone in the case of a uniform quantization for a random variable modeled by a Laplace distribution is described. The method of Lagrange multiplier is applied for the entropy constrained minimization of the distortion. It provides an explicit formula for the λ multiplier and a surprisingly simple expression is obtained for both the rate R and the distortion D. Then a bound for the Rate-Distortion R(D) function is derived, and compared with already known approximations toward low or high bitrates. These new results provide a more accurate description of the quantization behavior, to improve MPEG-like encoder compression performances. Direct applications to compression are mentioned, but not described in this paper.