Digital Subscriber Line Terminals for Use with Correlated Line Codes

This paper is a mathematical analysis of digital subscriber lines that use adaptive decision feedback equalization (DFE). Adaptive transversal feedforward filters (FFF) and feedback filters (FBF) with baud rate sampling are assumed. In order that all block codes are considered in the model, correlation between the values of the transmitted symbol values is included. Additionally, added noise is not assumed to be white, to permit the eyaluation of the effects of near end crosstalk and residual echo noise. It is shown that the correlation between the transmitted symbols causes the FBF to adapt differently than they usually do (i.e., cancel intersymbol interference within the range of the FBF) in two ways: the FBF uses the correlation between transmitted symbols to reduce the intersymbol interference outside of its range, and a bias vector is added to the FBF tap weights that adjusts future slicing levels to account for the variable likelihood of future transmitted symbol values. It is found that the received signal-to-noise ratio is approximately a linear function of loop insertion loss when the loss is high and noise is low.