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×1 vector input, A is the M×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=Σ_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). 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