Optimum orthogonal quantization of signal space (Corresp.)

Orthogonal quantization is a partition of signal space that is achieved by independent quantization of each of its orthogonal axes. A closed form expression is derived for the quantized channel cutoff rate and for the optimum orthogonal quantization similar to the one that has been derived for binary signaling. While orthogonal quantization is natural for communication systems in which the transmitted signals are themselves orthogonal, it can also be profitably applied to other signals, e.g., a simplex set in a lower dimensional space. Though orthogonal quantization is inferior to optimal quantization, it is essentially simpler and does not incur great loss in performance. A numerical example illustrates the relative merits of optimal and orthogonal quantization for the simplex set in the plane.