INFORMATION RATES FOR THE PEAK-LIMITED AND SLOPE-LIMITED MAGNETIZATION MODEL WITH BINARY SIGNALING

Lower bounds on the capacity and the cut-off rate are derived for the recently introduced peak- and slope-limited magnetization model when r estricted to binary pulse amplitude modulated (PAM) inputs. The inform ation carrying binary PAM resembles the common practice in magnetic re cording where multi-level signalling is rarely used. For the slope dom inated region, where the ''temporal'' restrictions are imposed solely by the slope constraint, the achievable rates, as predicted by the low er bounds on either the capacity or the cut-off rate, are proportional to the cube root of a properly defined signal-to-noise ratio. The sam e trend is demonstrated for some specific simple uncoded and coded sys tems where in the latter a punctured binary convolutional code with a constant rate independent of the signal to noise ratio, is employed. I n the channel dominated region where the slope constraint is relaxed, the achievable rates increase logarithmically with a properly defined signal-to-noise ratio. The same functional behavior for both the slope as well as the channel dominated regions is evidenced even when relax ing the restriction of binary PAM signalling and allowing for arbitrar y peak (or even average) power and slope limited modulations. These ob servations provide a theoretical support to the use of the practically appealing binary PAM in those recording systems which can reasonably be characterized by the peak- and slope-limited model.