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This paper presents a simple differential speech signal coding algorithm, based on backward adaptation. The considered algorithm is executed in frame by frame manner, by implementing predictive and adaptive quantization techniques. Both prediction and adaptation are performed backward, based on the previously quantized input signal frame. This enables us to obtain high quality output signal, without increasing the bit rate. This research puts emphasis on the quantizer design, with the optimal support limit determination, and theoretical performance evaluation. Objective quality of the output signal is evaluated through signal to quantization noise ratio (SQNR). We perform theoretical and experimental analysis of the algorithm performance and provide comparative results of implementing speech signal coding techniques with similar complexity. Experimental results show that our simple differential speech coding algorithm satisfies the G.712 Recommendation for high-quality speech coding at the bit rate of 6 bits per sample. This indicates that the algorithm can be successfully implemented in high quality speech signal coding.

The problem we address in this paper is the design of a quantizer that in comparison to the classical fixed-rate scalar quantizers provides more sophisticated bit rate reduction while restricting the class of quantizers to be scalar. We propose a switched variable-length code (VLC) optimal companding quantizer composed of two optimal companding scalar quantizers, the inner and the outer one, both designed for the memoryless Gaussian source of unit variance. Quantizers composing the proposed quantizer have a different codebook sizes and a different compressor functions. Particularly, we assume a smaller size of the inner quantizer's codebook in order to provide assignment of the shorter codewords to the high probability low amplitude speech samples belonging to the support region of the inner quantizer. We study the influence of codebook size of the inner and the outer quantizer on the Signal to Quantization Noise Ratio (SQNR). In such a manner the conclusion of the proposed quantizer significance in speech compression is distinctly shown in the paper. For the proposed quantizer model and its forward adaptive version the SQNR robustness analysis in a wide variance range is also presented in the paper. It is shown that our multi-resolution quantizer can satisfy G.712 Recommendation for high-quality quantization at the bit rate of 6.3 bit/sample achieving the compression of 1.7 bit/sample over the G.711 quantizer.