18. Efficient Multiplex for Band-Limited Channels: Galois-Field Multiple Access

A new efficient-bandwidth code-divison multiple access CDMA for bandlimited channels is introduced,
which is based on finite field transforms. A multilevel code division multiplex exploits
orthogonality properties of non binary sequences defined over a complex finite field.
Galois-Fourier transforms contain some redundancy and only cyclotomic coefficients are needed
to be transmitted yielding compact spectrum requirements. The primary advantage of such schemes
regarding classical multiplex is their better spectral efficiency.
This paper estimates the bandwidth compactness factor relatively to time division multiplex access TDMA
showing that it strongly depends on the alphabet extension. These multiplex schemes termed
Galois-field division multiplex GDM are based on transforms for which there exists fast algorithms.
They are also convenient from the hardware viewpoint since they can be implemented by a digital signal processor.