Abstract: A trellis code of a special class is encoded by employing a binary convolutional code with a small constraint length, followed by a convolutional processor and a signal mapper. The trellis code is decoded by the trellis of the binary convolutional code.

Abstract: This invention is a decoding method for a special class of trellis codes which have large free distances. The encoding of the trellis code to be decoded can be implemented by employing a single binary convolutional code followed by more than one processor. The decoding can be implemented by using the trellis of the binary convolutional code and additional processors.

Abstract: This invention is a multilevel trellis coding method which employs a single binary convolutional code and is called a single-stage and multilevel trellis coding. This invention can be generalized by combining several single-stage multilevel codings together to form a multilevel trellis coding for which the number of stages is less than the number of coding levels. New trellis coded modulation systems and binary trellis coding systems which are designed by the aforementioned trellis coding method are better than the currently known coding systems if the communication channels are additive white Gaussian noise (AWGN) channels.