Random matrices in information theory and coding

We describe some scenarios of practical interest in wireless communication systems, and their relationship with problems involving random matrices. In this context we discuss some recent results on the distribution of the eigenvalues of Wishart and Gaussian unitary random matrices, their application for the analysis of the Shannon capacity of Multiple-Input Multiple-Output (MIMO) systems and for model order selection in wireless networks. Then, we describe some issues regarding the design of graph-based error correcting codes, where large sparse matrix on GF(q) are used as parity check matrices (Low-Density Parity-Check (LDPC) codes). We present a framework for the analysis of frame synchronization, where the detection of synchronization words is based on a sequential algorithm, and where the received symbols are corrupted by noise.