Linearization of Optimal Compressor Function and Design of Piecewise Linear Compandor for Gaussian Source

The constraints on the quantizer model are usually related to how complex the model can be designed and implemented. For the given bit rate, it is desirable to provide the highest possible signal to quantization noise ratio (SQNR) with reasonable complexity of a quantizer model. In order to avoid the influence of compressor function nonlinearity and the difficulties appearing in implementing and designing, especially in the Gaussian probability density function case, in this paper we linearize the optimal compressor function within the segments. We take advantage of piecewise linearization of the optimal compressor function, as a convenient solution for less complex designing compared to the asymptotically optimal compandor, and we provide performances close to the ones of the asymptotically optimal compandor. This makes our model useful in applications where the design and implementation complexity is a decisive factor. We propose a piecewise linear compandor (PLC) with an equal number of reproduction levels per nonuniformly spaced segments, where the segment thresholds are allotted to the equidistant optimal compressor function values. We study how the number of segments affects SQNR of the PLC. Features of the proposed PLC indicate its theoretical and practical significance in quantization of Gaussian source signals.