In the description of the Max-Log-MAP, we will follow the reasoning presented in [Vit98].
We consider the system model shown in Fig.1.


Fig. 1. System model

A binary message sequence is given by


where t is the message symbol at time t and is the sequence length. We assume that the message symbols are independently generated binary symbols and have equal a priori probabilities. The encoding operation can be graphically represented by state and trellis diagrams.