Optimal signature sets for transmission of correlated data over a multiple access channel

For multiple transmitters sending independent data to a single receiver, by modulating their data symbols with fixed length codewords, the problem of optimizing these codewords to maximize capacity has been addressed by S. Verdu (Proc. 24th Allerton Conf. on Comm., Control and Computing, 1989) and P. Viswanath and V. Anantharam (IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 1984-1991, 1999). This paper considers an analogous scenario when the information sent by the transmitters is correlated. The optimal codeword set and power allocation which minimizes TMSE (total mean square error) at the receiver under a total power constraint have been derived. The equivalence between TMSE and sum capacity is also shown, in the sense that minimizing the former corresponds to maximizing the latter.