Upper bounds for binary and ternary decision feedback equalization of the magnetic recording channel

A new technique proposed by Altekar and Beaulieu (see IEEE Trans. Inform. Theory, vol.39, p.145-56, Jan. 1993) for determining the upper bound to the probability of error of a decision feedback equalizer is applied to the magnetic recording channel (MRC). The upper bound on the probability of a symbol error is calculated as a function of the channel information density for both binary and ternary decision feedback equalization of the MRC. The MRC is modeled as a linear channel with a Lorentzian step response, additive white Gaussian noise, and perfect timing. A comparison of the binary and ternary MRC under these assumptions shows that in the absence of channel coding, the binary MRC is preferred for information densities of interest. However, the ternary MRC may have an advantage when channel coding is used at high information densities