THE INFORMATION CAPACITY OF A MULTIDIMENSIONAL 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 exceed that of a conventional temporal communications system with the same bandwidth. For imaging systems, an invariance theorem is proposed. This theorem explains the principles behind optical super-resolution. The theorem is applied to the analysis of analytic continuation and several previous results are predicted. The exploitation of multiple dimensions in communications is discussed. The spatial dimensions of communications systems are expected to become important if future communication needs are to be satisfied.