Universal Incremental Slepian-Wolf Coding

We present a strategy for Slepian-Wolf coding when the joint distribution of the sources is unknown. The encoders use an incremental transmission policy, and the decoder a universal sequential decision test. We show that the decoder is able to decode shortly after the rates of transmission exceed the Slepian-Wolf bounds. The decoder then send an ACK back to the encoders, terminating transmission. As the timing of this ACK depends on the unknown statistics, the duration of the transmission is unknown in advance. Therefore, the scheme is variable-rate. It adapts its transmission rates to match the unknown joint entropy of the sources. We show how to apply these ideas in the rate distortion context of Wyner-Ziv coding. We specify an incremental universal coding strategy. We show that in the case of unknown, but jointly Gaussian statistics, there is no rate-loss in comparison with the case of fully known statistics.