Trellis code construction for the joint source-channel problem

Summary form only given, as follows. The theory of source coding with a fidelity criterion for the noiseless channel establishes the existence of codes which permits to achieve the theoretical "rate-distortion" function. In general, the most known algorithms for vector quantization can be divided into two groups: block codes of length N and sliding block codes more commonly named trellis codes. Trellis codes have been intensively studied in their theoretical and practical aspects. Although both classes of source codes have the same performance for very long blocks (asymptotical assumption), for constrained length, trellis codes outperform block codes but with a greater complexity. The development of very fast VLSI technologies made the application of trellis coding very interesting and the complexity aspects became quickly unimportant. Under the high-rate hypothesis (high number of representatives per dimension of the vector quantizer) it can be proved that with increasing complexity the ultimate limit of the rate-distortion function can be approached. In this approach the granular and boundary gains are presented as duals of respectively the shaping and coding gains in data transmission applications.