SNR Merits of Binary Modulation Codes in Equalized Digital Recording Systems

For a digital recording system with binary modulation encoder and a linearly dispersive channel with additive noise, this paper determines optimum mean-square performances of the linear, partial-response, and decision-feedback equalizers. The analysis revolves around the power spectral density A(Ω) of the code and the folded signal-to-noise ratio X(Ω) of the channel. The latter function is analyzed for stylized optical and magnetic recording channels. For all equalizers it is shown that the effect of coding is akin to increasing X(Ω) by an additive portion 1/A(Ω). This favors depressions of A(Ω) at frequencies where X(Ω) is poor. However, for A(Ω) to have any depressions, the signaling rate must be increased with respect to uncoded storage, and this inevitably degrades X(Ω). At high information densities the degradation is often too large for coding to be rewarding. Examples serve to illustrate these results.