An Approximate Closed-Form Expression for Calculating Performance of Floating-Point Format for the Laplacian Source

This paper introduces a novel approach that bridges the floating-point (FP) format, widely utilized in diverse fields for data representation, with the μ-law companding quantizer, proposing a method for designing and linearizing the μ-law companding quantizer to yield a piecewise uniform quantizer tailored to the FP format. A key outcome of the paper is a closed-form approximate expression for closely and efficiently evaluating the FP format’s performance for data with the Laplacian distribution. This expression offers generality across various bit rates and data variances, markedly reducing the computational complexity of FP performance evaluation compared to prior methods reliant on summation of a large number of terms. By facilitating the evaluation of FP format performance, this research substantially aids in the selection of the optimal bit rates, crucial for digital representation quality, dynamic range, computational overhead, and energy efficiency. The numerical calculations spanning a wide range of data variances provided for some commonly used FP versions with an 8-bit exponent have demonstrated that the proposed closed-form expression closely approximates FP format performance.