Binary Signaling of Correlated Sources Over Orthogonal Multiple-Access Channels

The optimal energy allocations for minimizing the joint symbol error rate for binary signaling of two correlated sources over the orthogonal multiple-access Gaussian channel under joint maximum a priori (MAP) detection are determined. An exact expression for the system's probability of joint symbol error, as well as its union bound, is derived. Analytic minimization of the union bound reveals that the optimal energy allocation coincides with that of nonuniform binary signaling over the single-user additive white Gaussian noise channel. It is also shown numerically that the optimal energies that minimize the union bound also minimize the exact probability of error. Finally, it is shown via simulations for strongly biased sources that the use of joint MAP detection over two independent single-user systems leads to significant gains.