A speech signal coding system comprises a prediction filter coupled with an output of a quantizer for prediction of a signal. A subtractor provides the difference between an input signal and an output of the prediction filter. A quantizer quantizes the residual signal, which is the difference provided by the subtractor. The quantizer is improved by adaptively adjusting step size for quantization. Thus, the coded outputs, according to the present invention, are the parameter information of the prediction filter, quantized output of the residual signal, and step information for quantization. The quantization step is determined according to the fundamental step size which provides the statistical variance, equal to one, to the quantized signal, and/or the power of the residual signal. Because of an efficient encoding with an adaptive control of the quantization step, the bandwidth for transmission of the coded signal in a communication system or transmission rate of coded speech signal is minimized. Excellent speech is reproduced through a narrow band channel, or low bit rate digital channel like 16 kbits/second digital channel.