Finite Blocklength Analysis for Optical Fiber MIMO Channels

The multiple-input and multiple-output (MIMO) technique is considered as a promising approach for improving the throughput and reliability of optical fiber communications. However, the finite blocklength (FBL) analysis of optical fiber MIMO systems is not available in the literature. Considering the Jacobi MIMO channel, which was proposed to model the nearly lossless propagation and the crosstalks in optical fiber channels, this paper studies the optimal average error probability (OAEP) of optical fiber multicore/multimode systems in the FBL regime. In particular, we consider the case where the coding rate is in the O (1/√ LM) proximity of the capacity, with M and L denoting the number of transmit channels and blocklength, respectively. To this end, a central limit theorem (CLT) for the information density is first established in the asymptotic regime where the blocklength and the number of transmit, receive, and available channels approach infinity with fixed ratios. With the aid of the CLT, the closed-form upper and lower bounds for the OAEP with the concerned rate are then derived. It is shown that the derived bounds could degenerate to those for Rayleigh MIMO channels if the number of available channels goes to infinity. Numerical simulations indicate that the derived bounds are closer to the performance of low-density parity check (LDPC) coding schemes than outage probability, thus providing a better characterization with the concerned the rate.