The information capacity of a multi-dimensional communications system

One-dimensional communications and two-dimensional optics may be considered special cases of a multi-dimensional communications system, the information capacity and channel capacity of which are derived. It is shown that the channel capacity of such a system may far exceed that of a conventional temporal communications system with the same bandwidth. In the case of imaging systems, an invariance theorem is proposed. This theorem is then invoked to explain the underlying principles behind optical super-resolution. The theorem is then applied to the analysis of analytic continuation and several previous results are predicted. The exploitation of multiple dimensions in communications is also discussed. The spatial dimensions of communications systems are expected to become increasingly important if future communication needs are to be satisfied.