The error exponent is an important metric to understand the performance of a communication system. Indeed, it gives expression to the trade-off that exists between the average block-error probability (corresponding to the optimum code) and the required coding length at a prescribed rate below the channel capacity.
Owing to the difficulty in evaluating it, bounds have been proposed since early stage of information-theoretic analysis of communication systems. Among these, the largely adopted Random Coding Error Exponent (RCEE), proposed by Gallager, is based on random selection of the codewords with equal weight. Its refined version assumes that bad codewords are expurgated from the actual set of codewords in order to decrease the error probability.
In the case of MIMO channels, evaluation of the error exponent hinges upon the exploitation of Harish-Chandra-Itzykon-Zuber (HCIZ)-like integrals on matrix spaces, and it has been carried out in some particular scenarios with Rayleigh fading.
In this talk, expressions for Gallager's Random Coding Error Exponent (RCEE) and the corresponding Expurgated Error Exponent (EEE) are derived in a unifying framework, as functions only of the squared singular values of the channel matrix. The results encompass spatially Kronecker-correlated Rayleigh channels, line-of-sight MIMO systems, multiple-scattering channels, multi-hop amplify and forward MIMO channels with non-noisy relays and noisy destination. As an instance of application of our framework, we consider a multiple-scattering Rayleigh MIMO channels, with an arbitrary but finite number of scattering stages and channel state information (CSI) available at the receiver only. In this scenario, we evaluate closed-form expressions for both RCEE and EEE in terms of Meijer's G functions.

Giusi Alfano received Laurea degree in Communication Engineering from University of Naples "Federico II" Italy, in 2001, and the phd degree in Information Engineering in 2007 from University of Benevento, Italy. She is currently holding a post-doc position at Politecnico di Torino, Italy. Her research work lies mainly in the field of information-theoretic characterization of MIMO point-to-point links and wireless networks. Giusi was visiting researcher at ftw and TUW, Wien, from 2007 to 2010 and ERCIM fellow at NTNU Trondheim in 2011. In 2014, she has been visiting ERC chair on Noncommutative Distributions in Quantum Probability, Saarbrucken. She actively collaborates with Theoretic Communication Chair in Dresden.