Iterative algorithm for designing asymptotically optimal uniform scalar quantisation of the one‐sided Rayleigh density

Abstract

Abstract Design of optimal and asymptotically optimal quantisation subject to the mean squared error (MSE) criterion is a complex issue, even in the case of uniform scalar quantisation (USQ). The reason is that the MSE distortion dependence on the key designing parameter of USQ for source densities with infinite supports are complex and limit analytical optimisation of USQs. This issue of USQ design has been addressed for some source densities derived from the generalised gamma density. However, to the best of our knowledge, USQ for the one‐sided Rayleigh density has not been studied in detail. This has prompted our research so that this study provides a detailed analysis of USQ for the one‐sided Rayleigh density and proposes an iterative algorithm for its asymptotically optimal design. To estimate signal to quantisation noise ratio, we derive an asymptotic formula having reasonable accuracy for rates higher than 3 bits/sample. Our analysis can be useful in digital‐to‐analogue and analogue‐to‐digital conversion in diversity systems, orthogonal frequency division multiplexing systems and medical image processing.

Keywords

• Signal processing and detection
• Optimisation techniques
• Interpolation and function approximation (numerical analysis)
• Digital signal processing
• Optimisation techniques
• Interpolation and function approximation (numerical analysis)