On extremely high density digital recording

Several recording systems now operate at 10⁶bits per square inch; their performance is partly governed by mechanical defects. The efficiency of systems without such defects would be determined by the signal-to-noise ratio. We show that reliable operation at 10⁷bits per square inch is then possible and this, for example, might make tape-area-efficient broadcast-quality digital video recorders feasible. The ultimate densities given by information theory are demonstrated to be in the range 10⁸- 10⁹bits per square inch.