Minimum redundancy zero-error source coding with side information

We consider the design of instantaneous variable-length zero-error codes where the decoder has access to side information about the source, which is not available to the encoder. We show that finding the optimal code, which minimizes the expected codeword length, is an NP-hard problem. We derive an exponential-time optimal design algorithm. We also provide polynomial-time approximate algorithms, and discuss their average-case and worst-case performance guarantees.