An Efficient Coding Scheme for the MIMO Channel With Noisy Feedback and Its Security Analysis

In this paper, we propose a Schalkwijk-Kailath-type coding scheme for the multiple-input multiple-output (MIMO) channel with noisy feedback, and derive the corresponding achievable rate under fixed coding blocklength and the receiver's decoding error probability. Furthermore, we explore the security performance of the proposed scheme by considering the model in the presence of one or more external eavesdroppers, and provide ways to find the minimum coding blocklength achieving the security threshold of the system when the perfect/imperfect channel state information (CSI) of eavesdropping channel is known by the transmitter. Experimental results show that when the feedback power is sufficiently large, the achievable rate almost approaches the Shannon limit. Besides this, when the transmitter only knows an estimation of the eavesdropping channel's CSI, the security threshold of the system can still be achieved by choosing a larger coding blocklength.