Reliability Distributions of Truncated Max-log-map (MLM) Detectors Applied to ISI Channels

TL;DR

This paper derives exact and efficiently computable reliability distributions for truncated max-log-map detectors in ISI channels, enabling improved analysis of sliding-window MLM implementations.

Contribution

It provides a novel, general method to compute joint reliability distributions for truncated MLM detectors, accommodating various practical scenarios.

Findings

Exact expressions for joint MLM reliabilities and error probabilities

Efficient Monte-Carlo evaluation using eigenvalue decomposition

Applicable to diverse noise models and coding schemes

Abstract

The max-log-map (MLM) receiver is an approximated version of the well-known, Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. The MLM algorithm is attractive due to its implementation simplicity. In practice, sliding-window implementations are preferred; these practical implementations consider truncated signaling neighborhoods around each transmission time instant. In this paper, we consider sliding-window MLM receivers, where for any integer m, the MLM detector is truncated to a length- m signaling neighborhood. For any number n of chosen times instants, we derive exact expressions for both i) the joint distribution of the MLM symbol reliabilities, and ii) the joint probability of the erroneous MLM symbol detections. We show that the obtained expressions can be efficiently evaluated using Monte-Carlo techniques. Our proposed method is efficient; the most computationally expensive operation (in each Monte-Carlo trial) is an eigenvalue decomposition of a size 2mn by 2mn matrix. Practical truncation lengths can be easily handled. Finally, our proposed method is extremely general, and various scenarios such as correlated noise distributions, modulation coding, etc. may be easily accommodated.