Error exponents for the Gaussian Multiple-Access Channel

We give random-coding error-exponent bounds for the Gaussian Multiple-Access Channel (GMAC) Y = AX + N, where X is the K x 1 vector input, A is the M x K channel matrix, and N is a zero-mean Gaussian vector with full-rank covariance matrix N. The K users signal independently of each other, and the power of the k(th) user is P(k) = E{X(k)(2)}. This vector-valued channel is a generalization of the scalar-valued conventional GMAC, Y = Sigma(k=1)(K) X(k) + N, for which A = [1 ... 1]; it arises in multiuser signaling schemes such as Code-Division and Bandwidth-Efficient Multiple Access (CDMA and BEMA) [1], Error exponents give not only the capacity region of the channel, but also an indication of how the average probability of error decays as a function of the block length of random codes.