Analog diversity coding to provide transparent self-healing communication networks

The optimal use of the discrete Fourier transform (DFT) to perform analog diversity coding is described. It is shown that the DFT is a continuous-amplitude maximum-distance separable code over the field of complex numbers when the transform kernel is a prime root of unity. Electrical and optoelectronic implementations of the coding are discussed. It is shown that straightforward signal estimation can enhance the performance of analog diversity coding systems in the presence of channel noise by making use of the information in the remaining M-n channels when n link failures occur in an analog diversity coding system of N data channels. With least-squares estimation, and with an added complexity factor of M/N multiply/add operations, the noise power after estimation is reduced by 3 dB for n=1, or by 10 dB or more for 1