Joint source and noisy channel trellis encoding

In a trellis encoding communication system the decoder is a time-invariant nonlinear filter with finite memory (sliding-block code), and the encoder is a trellis search algorithm matched to the decoder. A coding theorem is established for a trellis encoding of a stationary and ergodic source over a discrete memoryless noisy channel which shows that such communication systems can perform arbitrarily close to the source distortion-rate function evaluated at the channel capacity.