On Computing Verdú's Upper Bound for a Class of Maximum-Likelihood Multiuser Detection and Sequence Detection Problems

The upper bound derived by Verdú is often used to evaluate the bit error performance of both the maximum-likelihood (ML) sequence detector for single-user systems and the ML multiuser detector for code-division multiple-access (CDMA) systems. This upper bound, which is based on the concept of indecomposable error vectors (IEVs), can be expensive to compute because in general the IEVs may only be obtained using an exhaustive search. In this correspondence, we consider the identification of IEVs for a particular class of ML detection problems commonly encountered in communications. By exploiting the properties of the IEVs for this case, we develop an IEV generation algorithm which has a complexity substantially lower than that of the exhaustive search. We also show that for specific communication systems, such as duobinary signaling, the expressions of Verdú's upper bound can be considerably simplified.