Decision feedback equalization and capacity on the linear stationary Gaussian channel

The capacity of a additive white Gaussian noise channel subject to bandwidth or filtering constraint is a classical problem of information theory. Recently, it has been shown that the relationship between the channel capacity for this channel and the variance achieved by the idealized unbiased minimum mean square error decision feedback equalizer (UMMSE-DFE) is the same as the relationship between the channel capacity for memoryless additive white Gaussian noise channel and the noise variance for that channel. This result indicates that the SNR of the UMMSE-DFE is the natural canonical SNR for the bandlimited channel. In this note, this important result is rederived in a manner that helps to further clarify the relationship between the estimator and capacity