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This paper addresses the issue of robust decoding of arithmetic codes. We first analyze dependencies between the variables involved in arithmetic coding by means of the Bayesian formalism. This provides a suitable framework for designing a soft decoding algorithm that provides high error-resilience. It also provides a natural setting for "soft synchronization", i.e., to introduce anchors favoring the likelihood of "synchronized" paths. In order to maintain the complexity of the estimation within a realistic range, a simple, yet efficient, pruning method is described. Models and algorithms are then applied to context-based arithmetic coding widely used in practical systems (e.g. JPEG-2000). Experimentation results with both theoretical sources and with real images coded with JPEG-2000 reveal very good error resilience performances.