Theory of an Imperfect PCM Encoder-Decoder Pair Using Half-Channel Measures

A theory is presented for the quantization noise power and gain of a PCM channel in terms of static and dynamic errors in encoder decision levels and decoder output levels. Decision profiles are used in a statistical model for encoder imperfections, while conditional output distributions describe those of the decoder. The model describes the combined behavior of any encoder and decoder that have been characterized separately in terms of the CCITT-defined half-channel tests. A linear regression model is used and the noise powers and offsets are shown to obey addition laws, while the gains obey a multiplicative rule.