Error exponents analysis for dual-hop η-μ Fading channel with amplify-and-forward relaying

In this paper, we investigate the error exponents of dual-hop amplify-and-forward (AF) system for η-μ fading channel. Channel capacity of a wireless communication system gives only the knowledge of maximum achievable rate. Therefore, it is necessary to analyse the decoding complexity of the code that achieves a certain level of reliable communication. In fact, a measure of reliability called error exponent exists which sets ultimate bounds on the performance of communication systems employing codes of finite complexity. Assuming the receiver has full channel state information (CSI) and the transmitter has no CSI, we derive the novel exact expressions of Random coding error exponent (RCEE) and expurgated error exponent which provide insight into an elementary tradeoff between the communication reliability and information rate. Moreover, the necessary codeword length can be computed easily without the extensive Monte-Carlo simulation to achieve predefined error probability at a given rate. Meanwhile, simplified approximate expressions in the high signal-to-noise ratio (SNR) regime are also obtained. In addition, we derive the exact closed-form expressions for the ergodic capacity and cutoff rate.