This work studies a novel power-efficient precoder design problem for a linear cellular array with base station (BS) cooperation: data symbols intended for mobile stations (MSs) are drawn from discrete finite alphabets, precoding is performed among BSs to produce appropriate signals transmitted over the channel, symbol-by-symbol detection is performed at each MS, and a minimum Symbol Error Probability (SEP) for detection is introduced as the Quality-of-Service (QoS) metric at each MS. With regular constellations such as 16-QAM deployed as system data inputs, the SEP constraints are formulated and characterized by a set of convex relaxations on the received signals. A convex power optimization problem is then formulated subject to the SEP constraints. By the primal-dual decomposition approach, a distributed algorithm is developed to solve the problem in which only local communication among BSs is required. Our scheme is shown to significantly outperform linear zero-forcing precoder in terms of transmit power consumption.