Accumulation of distortion in tandem communication links

The mean-square errors (mse) of individual links of a communication network generally do not add up to the overall mse because of mutual correlations among the errors on the individual links. This makes it difficult to interpret the magnitude of contribution of each link to the mse. It is shown that if the mse of each link is defined alternatively as the mse between conditional mean estimators of the original signal at the input and output of that link, then the overall mse is in fact the sum of the mse's on individual links. Several examples illustrate the usefulness of this principle, particularly in digital communications, in understanding the source of system impairments.