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Multiple access channels with arbitrarily correlated sources

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3 Author(s)

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 function p(u,v) and common part w=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 functions p(s), p(x_{1}|s,u),p(x_{2}|s,v) , such that H(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.

Published in:

IEEE Transactions on Information Theory  (Volume:26 ,  Issue: 6 )