Reliability Distributions of Truncated Max-Log-MAP (MLM) Detectors Applied to Binary ISI Channels

The max-log-MAP (MLM) receiver is an approximated version of the well-known Bahl-Cocke-Jelinek-Raviv algorithm. The MLM algorithm is attractive due to its implementation simplicity. In practice, sliding-window implementations are preferred, whereby truncated signaling neighborhoods (around each transmission time instant) are considered. In this paper, we consider binary signaling sliding-window MLM receivers, where the MLM detector is truncated to a length-m signaling neighborhood. Here, truncation is used to ease the burden of analysis. For any number n of chosen times instants, we derive exact expressions for both 1) the joint distribution of the MLM symbol reliabilities, and 2) the joint probability of the erroneous MLM symbol detections. We show that the obtained expressions can be efficiently evaluated using Monte-Carlo techniques. The most computationally expensive operation (in each Monte-Carlo trial) is an eigenvalue decomposition of a size 2mn×2mn matrix. The proposed method handles various scenarios such as correlated noise distributions, modulation coding, etc.