Two trellis coding schemes for large free distances

A trellis code encoded by using the encoder of a convolutional code C with a short constraint length followed by an additional processing unit is equivalent to a trellis code with a large constraint-length. In 1993, Hellstern proposed a trellis coding scheme for which the processing unit consists of a delay processor and a signal mapper. With Hellstern's scheme, trellis codes with large free distances can be constructed. In this paper, we propose two trellis coding schemes. For the first scheme, the processing unit is composed of multiple pairs of delay processors and signal mappers. For the second scheme, the processing unit is composed of a convolutional processor and a signal mapper, where a convolutional processor is a rate 1 convolutional code. The trellis code constructed from each of the proposed schemes can be suboptimally decoded by using the trellis of the convolutional code C with some feedback information. Either of the proposed schemes can produce a trellis code that has a larger bound on free distance and better error performance as compared to the trellis code constructed from Hellstern's scheme based on the same convolutional code C.