The Gallager Bound in Fiber Optical MIMO

The Multiple Input Multiple Output (MIMO) technique in fiber optical networks is a promising technology for up scaling networks' capabilities. Therefore, effective bounds on the error probability of finite length codewords are increasingly important. In this paper, we use random matrix techniques to obtain an analytic result for the Gallager bound error exponent for the fiber optical MIMO channel in the limit that the size of the codeword increases to infinity at a fixed ratio with the transmitter array dimensions. We assume zero backscattering inside the fiber which makes the transmission coefficients between the modes, elements of a unitary matrix. Moreover, the channel can be modelled a a random Haar unitary matrix between N transmitting and K receiving modes respectively, due to the scattering between modes.