Zero-error source-channel coding with source side information at the decoder

This paper describes the zero-error source-channel coding with source side information at the decoder. To analyze the zero-error scenario, we define the following graphs: the source confusability graph G_u and channel characteristic graph G_x. We can always find a code from a source graph to its complement. Separate source and channel coding corresponds to first mapping from the source alphabet to an index set and then mapping from the index set to the channel alphabet. The size of the smallest index set that allows a zero-error source code is the chromatic number of G_u, χ(G_u). The largest index set from which we can map to the channel alphabet is the stability number of G_x, α(G_x).