Error exponents for Rayleigh fading multi-keyhole MIMO channels

Along with the channel capacity, the error exponent is one of the most important information-theoretic measures of reliability, as it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we derive the closed-form expressions for the Gallager's random coding and expurgated error exponents for Rayleigh fading multi-keyhole multiple-input multiple-output (MIMO) channels, which provides insight into an elementary tradeoff between the communication reliability and information rate. Moreover, we can easily compute the necessary codeword length without the extensive Monte-Carlo simulation to achieve predefined error probability at a given rate. In addition, we derive the exact closed-form expressions for the ergodic capacity and cutoff rate based on the easily computable Meijer G-function. We also quantify the effects of the number of antennas, channel coherence time and the number of keyholes on the required codeword length to achieve a certain decoding error probability.