This paper exploits a generic downlink symbiotic radio (SR) system, where a Base Station (BS) establishes a direct (primary) link with a receiver having an integrated backscatter device (BD). In order to accurately measure the backscatter link, the backscattered signal packets are designed to have finite blocklength. As such, the backscatter link in this SR system employs the finite block-length channel codes. According to different types of the backscatter symbol period and transmission rate, we investigate the non-cooperative and cooperative SR (i.e., NSR and CSR) systems, and derive their average achievable rate of the direct and backscatter links, respectively. We formulate two optimization problems, i.e., transmit power minimization and energy efficiency maximization. Due to the non-convex property of these formulated optimization problems, the semidefinite programming (SDP) relaxation and the successive convex approximation (SCA) are considered to design the transmit beamforming vector. Moreover, a low-complexity transmit beamforming structure is constructed to reduce the computational complexity of the SDP relaxed solution. Finally, the simulation results are demonstrated to validate the proposed schemes.Index Terms-Symbiotic radio (SR), backscatter, finite blocklength channel codes, semi-definite programming (SDP), successive convex approximation (SCA)