This paper considers the design of efficient quantizers for a robust distributed source coding system. The information is encoded at independent terminals and transmitted across separate channels, any of which may fail. The scenario subsumes a wide range of source and source-channel coding/quantization problems, including multiple descriptions and distributed source coding. Greedy descent methods depend heavily on initialization, and the presence of abundant (high density of) "poor" local optima on the cost surface strongly motivates the use of a global design algorithm. We propose a deterministic annealing approach for the design of all components of a generic robust distributed source coding system. Our approach avoids many poor local optima, is independent of initialization, and does not make any simplifying assumption on the underlying source distribution. Simulation results demonstrate a wide spread in the performance of greedy Lloyd-based algorithms, and considerable ga...