The use of multiple antenna arrays in transmission and reception has become an integral part of modern wireless communications. To quantify the performance of such systems, the evaluation of bounds on the error probability of realistic finite length codewords is important. In this paper, we analyze the standard Gallager error bound for both constraints of maximum average power and maximum instantaneous power. Applying techniques from random matrix theory, we obtain analytic expressions of the error exponent when the length of the codeword increases to infinity at a fixed ratio with the antenna array dimensions. Analyzing its behavior at rates close to the ergodic rate, we find that the Gallager error bound becomes asymptotically close to an upper error bound obtained recently by Hoydis et al. 2015. We also obtain an expression for the Gallager exponent in the case when the codelength spans several Rayleigh fading blocks, hence taking into account the situation when the channel varies during each transmission.

Technology is moving towards space division multiplexing in optical fiber to keep up the trend in rate increase over time and to avoid an imminent capacity crunch. Thus, it is of paramount interest to estimate the potential gains of this approach. As more spatial channels are being packed into a single fiber, the increased crosstalk necessitates the use of MIMO to guarantee reliable operation. In this paper, we exploit the analogy between an optical fiber and a model from mesoscopic physics - a chaotic cavity - to obtain a novel channel model for the optical fiber. The model captures both random distributed crosstalk and mode-dependent loss, which are described within the framework of scattering theory. Using tools from replica theory and random matrix theory, we derive the capacity of the fiber optical MIMO channel model.

Multiple-input and multiple-output processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes or multiple cores or both in the fiber. In this paper, we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant crosstalk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in the transmission may be parameterized by a number of unutilized channels in the fiber. We analyze the system in a dual fashion. First, we evaluate a closed-form expression for the outage probability, which is handy for small matrices. We also apply the asymptotic approach, in particular the Coulomb gas method from statistical mechanics, to obtain closed-form results for the ergodic mutual information, its variance as well as the outage probability for Gaussian input in the limit of large number of cores/modes. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.

MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. The lack of back-scattering necessitates the modeling of the transmission coefficients between modes as elements of a unitary matrix. Also, due to the scattering between modes the channel is modeled as a random Haar unitary matrix between Nttransmitting and Nrreceiving modes. In this paper, we apply a large-deviations approach from random matrix theory to obtain the outage capacity for Haar matrices in the low outage limit, which is appropriate for fiber-optical communications. This methodology is based on the Coulomb gas method for the eigenvalues of a matrix developed in statistical physics. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.