The two-dimensional block transform coding scheme based on the discrete cosine transform has been studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. In this paper we present a method for the joint source-channel coding optimization of a scheme based on the 2-D block cosine transform when the output of the encoder is to be transmitted via a memoryless binary symmetric channel. Our approach involves an iterative algorithm for the design of the quantizers (in the presence of channel errors) used for encoding the transform coefficients. This algorithm produces a set of locally optimum (in the mean squared- error sense) quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, we have used an algorithm based on the steepest descent method, which under certain covexity conditions on the performance of the channel-optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noisy channels have been obtained and appropriate comparisons against a reference system designed for no channel errors have been rendered. It is shown that substantial performance improvements can be obtained by using this scheme. Furthermore, theoretically predicted results for an assumed 2-D image model are provided.