An Information-Spectrum Approach to Weak Variable-Length Source Coding   with Side-Information
  This paper studies variable-length (VL) source coding of general sources with side-information. Novel one-shot coding theorems for coding with common side-information available at the encoder and the decoder and Slepian- Wolf (SW) coding (i.e., with side-information only at the decoder) are given, and then, are applied to asymptotic analyses of these coding problems. Especially, a general formula for the infimum of the coding rate asymptotically achievable by weak VL-SW coding (i.e., VL-SW coding with vanishing error probability) is derived. Further, the general formula is applied to investigating weak VL-SW coding of mixed sources. Our results derive and extend several known results on SW coding and weak VL coding, e.g., the optimal achievable rate of VL-SW coding for mixture of i.i.d. sources is given for countably infinite alphabet case with mild condition. In addition, the usefulness of the encoder side-information is investigated. Our result shows that if the encoder side-information is useless in weak VL coding then it is also useless even in the case where the error probability may be positive asymptotically. 
Shigeaki Kuzuoka and Shun Watanabe
cs.IT math.IT