The Multiple Access Channel with Correlated Sources and Cribbing Encoders

A discrete memoryless multiple access channel (MAC) is a quadruple { X1,X2, PY |X1,X2 ,Y } where X1,X2 are the input alphabets, Y the output alphabet, and PY |X1,X2 a transition probability matrix from X1 × X2 to Y . For shorthand notation, we will refer to the MAC by PY |X1,X2 . A source pair is a triplet {U ,V, PU,V } where PU,V is a distribution on U × V . We use the following notation: random variables are denoted by uppercase letters. Sequence of n letters from alphabet X is denoted by x, and the substring xi, xi+1, . . . , xj as x j i . When the dimension n is understood from the context, n-vectors are denoted by boldface letters: x = x. Similar notation holds for random variables and random vectors, e.g., V , U, U, etc. The channel and source are assumed memoryless, thus probabilities of n-sequences are given by