Hamming coding for Multiple Sources

We introduce Hamming Codes for Multiple Sources (HCMSs) as a potential solution of perfect Slepian-Wolf (SW) coding for arbitrary number of terminals. Moreover, we study the case with three sources in detail. We present the necessary conditions of a perfect SW code and show that there exists infinite number of HCMSs. Moreover, we show that for perfect SW code with sufficiently long code length, the compression rates of different sources can be trade-off flexibly.