Multiple access channels with arbitrarily correlated sources
Cover, T.; Gamal, A.E.; Salehi, M.
Information Theory, IEEE Transactions on
Volume 26, Issue 6, Nov 1980 Page(s): 648 - 657
Digital Object Identifier  
Summary: Let{(U_{i},V_{i})}_{i=1}^{n}be a source of independent identically distributed (i.i.d.) discrete random variables with joint probability mass functionp(u,v)and common partw=f(u)=g(v)in the sense of Witsenhausen, Gacs, and Körner. It is shown that such a source can be sent with arbitrarily small probability of error over a multiple access channel (MAC){cal X_{1} times cal X_{2},cal Y,p(y|x_{1},x_{2})},with allowed codes{x_{l}(u), x_{2}(v)}if there exist probability mass functionsp(s), p(x_{1}|s,u),p(x_{2}|s,v), such thatH(U|V)<I(X_{1}; Y|X_{2},V,S),H(V|U )<I(X_{2};Y|X_{1},U,S),H(U,V|W)<I(X_{1},X_{2};Y|W,S),H(U,V)<I(X_{1},X_{2};Y),mbox{where}p(s,u,v,x_{1},x_{2},y), Xl, X2, y)=p(s)p(u,v)p(x_{1}|u,s)p(x_{2}|v,s)p(y|x_{1},x_{2}).lifts region includes the multiple access channel region and the Slepian-Wolf data compression region as special cases.

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