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This paper investigates the performance of non-orthogonal multiple access (NOMA)-based coordinated direct and relay transmission (CDRT) networks with short-packet communications undergoing Nakagami- fading channels and subject to imperfect successive interference cancellation (SIC). To enhance the transmission reliability of a cell-edge user (CE) or a cell-center user (CU), a dynamic relay selection (RS) strategy is proposed, in which exact closed-form expressions are derived for the block-error-rate (BLER) of the users and system throughput. To obtain further insights, an asymptotic BLER analysis is carried out at high signal-to-noise ratio (SNR) regime, based on which the diversity orders are deduced. Numerical results are presented to corroborate the analytical results, and they show that: (i) the performance of the NOMA system outperforms its orthogonal multiple access (OMA) counterpart in terms …