Performance upper bounds for breadth first search detection over finite interference channels

We derive an upper bound on the bit error probability in breadth first limited search detection over a finite interference channel, which includes finite length ISI channels and multiuser channels as two special cases. We show that the bit error probability of the breadth first algorithm is bounded from above by the sum of three terms: the Forney (1972) upper bound on the error probability in the Viterbi algorithm (VA) detection and two upper bounds on the two types of the error probability caused by the correct path loss event. We also show that the error propagation (in terms of the mean recovery step number) is finite for all finite interference channels. The procedures can be applied to time variant interference channels in which the multiuser interference (MUI) channel is a special case. The results can also be used to construct convolutional codes for the M-algorithm.