The encoder performs the function of differentiation; a quantizer precedes the differencing of adjacent quantized samples; the decoder is an accumulator, which if correctly initialized exactly recovers the quantized signal.
The incorporation of the decoder inside the encoder allows quantization of the differences, including nonlinear quantization, in the encoder, as long as an approximate inverse quantizer is used appropriately in the receiver. When the quantizer is uniform, the decoder regenerates the differences implicitly, as in this simple diagram that Cutler showed:
U.S. patent 2605361, C. Chapin Cutler, "Differential Quantization of Communication Signals", filed June 29, 1950, issued July 29, 1952 https://patents.google.com/patent/US2605361 ↩