Error probability bound for reduced complexity multiuser decoding using orthogonal decomposability

We develop an upper bound on the error probability of the reduced-complexity group-metric multiuser convolutional decoder. This error bound results from discarding a class of redundant error sequences which are orthogonally decomposable. Indecomposable sequences for uncoded multiuser detection were introduced previously for the non-fading channel, and their enumeration is computationally intensive. By restricting attention to orthogonally decomposable error sequences for the fading channel, we can characterize sequences whose decomposability is independent of the fading parameters. Furthermore, we can easily compute this bound by evaluating the generating function of the encoder of the user in question