A vector trellis coded modulation scheme (VTCM) is accomplished by blocking input samples into a sequence of input vectors of length L, vector convolutional coding the input vectors to map K input vectors into N output vectors and modulating the output vectors into symbols from an expanded alphabet. In a first case, each output vector is modulated to a different symbol thereby improving coding gain while maintain bandwidth efficiency. In a second case, blocks of N output vectors are modulated to one symbol thereby improving bandwidth efficiency by a factor of N while maintain coding gain. A polyphase/multirate representation of the vector convolutional codes is preferably used to generated the vector convolutional codes. In general, a computer search can be employed to find the polyphase coefficients that define the set of vector convolutional codes. When the input and output vectors have the same length, known scalar-valued convolutional codes are blocked to generate the vector convolutional codes. This provides good modulation codes without having to perform a computer search.
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