Final Activity Report Summary - AI-COM (Approximate Inference in Graphical Models for Digital Communications) The goal of this project was to use new developments in approximate inference (artificial intelligence) for designing digital communication systems (AI-COM). The main three results have been: 1 Precoder optimisation: In ADSL and wireless systems we need to use a linear precoder to maximize the transmission rate. These precoders are designed to make the different channels independent. We have shown that correlating the inputs the transmission grows considerably, which can produce a considerable gain in the amount of information transmitted through any multiple-input multiple-output communication system. 2 Gaussian processes for designing digital communication receivers: Gaussian processes (GPs) are novel tools in machine learning for designing general detectors and estimators. We have shown that GP need shorter training sequence to achieve the same performance than other nonlinear detectors (e.g. neural networks or SVMs) and they provide accurate probability predictions, which are fundamental for the correct performance of communication receivers. 3 Joint source and channel coding: Low-Density Parity-Check (LDPC) codes have been shown to achieve channel capacity in the most interesting cases (Binary Erasure, Binary Symmetric and Gaussian channels), we have built on these codes to propose a code that compresses the information first with an LDPC code and then uses another to protect the source. We have shown that in the finite block length this joint scheme increases the transmission rate, compare to separate approach without an increase in the complexity. Ancillary results: We have shown a new method for estimating information theoretic quantities, as differential entropy, mutual information and the divergence, from samples. We have proven the convergence of our method using waiting times distributions.