An information-spectrum approach to weak variable-length Slepian-Wolf coding

In this paper, we investigate weak variable-length Slepian-Wolf (VL-SW) coding of general sources. First, by using the information-spectrum method, we show novel non-asymptotic trade-off between the error probability and the codeword length of VL-SW coding. Then, we give an asymptotic formula for the optimal coding rate achievable by VL-SW coding. Especially, we investigate VL-SW coding for mixed sources. Our results spotlights the fact that distinguishability between component sources plays an important role in adjusting the coding rate at the encoder. We also demonstrate that our general results derive a known formula for the optimal achievable rate of VL-SW coding for mixture of i.i.d. sources and extend to countably infinite alphabet case with mild condition.