On zero-error coding of correlated sources

The authors consider the following simple encoding scenario, which they term successive encoding: φ_x performs lossless encoding of X, at rate H(X), and φ_y is designed assuming that the decoder has recovered X. For coding with vanishing error probability, the results of Slepian and Wolf (1973) show that time-sharing of the two possible successive encoding scenarios (obtained by interchanging the roles of X and Y) is optimal, in that all achievable rate pairs can be achieved via this strategy. But time-sharing combined with successive encoding may not be an optimal strategy in the case of zero-error coding. The authors construct a simple example for this suboptimality phenomenon.