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To model the behavior of channels in real-world mobile systems, Ying introduced an extension of the π-calculus by taking channel noise into account. Unfortunately, this extension is not faithful in the sense that its semantics does not coincide with the standard one for the π-calculus in the noise-free case. In this paper, we consider a simple variant of the π-calculus, the asynchronous π-calculus (Aπ), which has been used for modeling some concurrent systems with asynchronous communication. To model these systems with noisy channels, we propose a faithful extension of Aπ, called the Aπn-calculus. After giving a probabilistic transitional semantics of Aπn, we introduce bisimilarity in Aπn and show that it is a partial input congruence. If a specification of a system is described as a process P in Aπ and we view the behavior of P in Aπn as an implementation of the specification, then it is interesting to measure how far the behavior in Aπn is from that in Aπ. We thus introduce the notion of reliability degree, which is based upon a new approximate bisimulation. We find that bisimilar agents may have different reliability degrees and even the agent with the greatest reliability degree may not be satisfactory. We thus appeal to Shannon's noisy channel coding theorem and show that reliability degrees can be improved by employing coding techniques.