Signal sets are created from available amplitude and phase modulations by indexing ordered subspaces. The subspaces need not be limited to the class of subspaces known as binary subspaces. The resultant signal sets, for a preselected power and bandwidth, are widely separated and unlikely to be confused by the effects of channel noise. Such signals can be in either finite block or convolutional form, depending on the natural format of the desired transmission. Further according to the invention are basic apparatus for encoding and modulating as well as demodulating and decoding a signal in accordance with the invention.; Specifically, a method is provided for decoding that incorporates a specific type of decoding/demodulation techniques which develops accurate estimates of the information from the received signal in a computationally efficient manner and which permits high speed operation using soft-decision decoders.