Due to the stringent requirement of low-latency, Finite-Blocklength Coding (FBC) has been developed to guarantee reliability in Ultra-Reliable and Low-Latency Communications (URLLC). However, ensuring the reliability and latency of FBC for downlink transmissions has remained as an open issue for URLLC with random arrivals. In this paper, we focus on a multi-user downlink system with URLLC required. In the downlink transmission, we obtain a benefit on the reliability from a longer blocklength, generated by grouping and jointly encoding the multi-users' packets. By this means, a Joint Framing and Finite-Blocklength Coding (JF <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> BC) scheme is proposed to provide the requirements of reliability and latency. In particular, considering the queueing effects for latency under random arrivals, we employ a cross-layer approach to characterize the JF <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> BC policy. Under the queue-aware policy, we show an optimal tradeoff between the queueing delay and reliability by a Linear Programming (LP) problem, in which a matrix-based algorithm is developed to automatically generate the LP problem for the multi-user scenario. To optimize the tail distribution of queueing delay, we further extend the optimal tradeoff by using the violation probability of maximal queue length as the delay measure.
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