In a trellis coding arrangement, the alphabet is comprised of a plurality of cosets of a sublattice of a p-dimensional lattice, where p<4.

Disclosed is a modem including a transmitter having a convolutional encoder for transforming each group interval digital data into an expanded bit sequence having symbol-selecting bits and a frame of subset-selecting bits forming a plurality of bit groups, with each bit group designating a 2-dimensional subset and the symbol-selecting bits being used to select one 2-dimensional symbol from each of the selected subsets, the transmitter further providing modulation of a carrier signal, and a receiver wherein a commonality-seeking, branch cost calculator determines the candidate branch associated with the minimum cost N-dimensional symbol subset for each coset and a Viterbi decoder which determines the maximum likelihood path from a plurality of surviving paths formed from branches selected from the candidate branches.

A reduced cost, robust data communication scheme for very small aperture terminal satellite communication systems combines non-coherent frequency detection and trellis-coded, multi-frequency modulation. The data code width is associated with the size of a multiple frequency set and the selection of a given combination of frequencies for transmission during a respective baud. One portion the data is convolutionally encoded and points to an orthogonal signal set associated with frequencies of a partitioned multiple frequency set. Another portion of the data identifies the frequency combination within the group pointed to by the one portion. The combined portions encode a multi-frequency transmission waveform. At the receiver, the multi-frequency tone sequence is detected by non-coherent frequency detection. For each baud, matched filters output a most likely set of frequencies transmitted during that baud, as soft decisions to a Viterbi decoder.

A reduced cost digital data modulation and demodulation scheme for very small aperture terminal (VSAT) satellite communication systems combines non-coherent frequency detection with trellis-coded, multi-frequency modulation. The technique is robust to phase noise and frequency uncertainty and is capable of achieving the performance of rate one-half phase shift keyed modulation. The code width of data to be transmitted bears a prescribed relationship to the size of a multiple frequency set and the selection of a given combination of frequencies within that set for transmission during a respective baud. One portion the data is convolutionally encoded and provides a pointer to one of plural groups of orthogonal signal sets associated with frequencies into which the multiple frequency set has been partitioned. Another portion of the data identifies the frequency combination within the group pointed to by the one portion. The combined portions encode a multi-frequency waveform transmitted to the receiver site. At the receiver site, the sequence of multi-frequency tones produced by the transmitter encoder is detected by non-coherent frequency detection. For each baud, the outputs of matched filters are examined to determine the most likely set of frequencies to have been transmitted during that baud. Most likely frequency combination determinations provide soft decision inputs to a Viterbi decoder.

A differentially encoded digital signal waveform is generated as a discrete time representation of a desired analog signal utilizing multi-frequency modulation techniques. The computational capability of present day, industry-standard microcomputers equipped with a floating point array processor or digital signal processor chip is utilized to perform digital frequency encoding and compute both discrete Fourier transforms and inverse discrete Fourier transforms to provide a transmitter and receiver system utilizing suitably programmed microcomputers coupled by a communications channel.