Lossless coding for distributed streaming sources

Distributed source coding is traditionally viewed in the block coding context -- all the source symbols are known in advance at the encoders. This paper instead considers a streaming setting in which iid source symbol pairs are revealed to the separate encoders in real time and need to be reconstructed at the decoder with some tolerable end-to-end delay using finite rate noiseless channels. A sequential random binning argument is used to derive a lower bound on the error exponent with delay and show that both ML decoding and universal decoding achieve the same positive error exponents inside the traditional Slepian-Wolf rate region. The error events are different from the block-coding error events and give rise to slightly different exponents. Because the sequential random binning scheme is also universal over delays, the resulting code eventually reconstructs every source symbol correctly with probability 1.