Trade-off of lossless source coding error exponents

We consider the lossless encoding of two simultaneous sources. The encoder may choose to discriminate against one source and hence the error exponents for the two sources can be different. The goal of this paper is to understand the region of achievable error-exponent pairs for lossless source coding. In the fixed-block-length case, the error exponent region is completely characterized and is found to be relatively trivial. However, in the streaming context, it is shown that there exists a non-trivial trade-off between the two error exponents. Both an inner bound and an outer bound are given for that case, but they do not match. The outer bound comes from a multi-stream version of the uncertainty-focusing bound.