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Ar{\i}kan's polar coding, is by now a well studied technique that allowsachieving the symmetric capacity of binary input memoryless channels with lowcomplexity encoding and decoding, provided that the polar decoding architectureis used and the decoding metric is matched to the true channel. In this paper,we analyze communication rates that are achievable when the polarcoding/decoding architecture is used with the decoder using an incorrect modelof the channel. We define the `polar mismatched capacity' as an analogue of theclassical mismatched capacity, give an expression for it, and derive bounds onit.

Channel capacity of polar coding with a given polar mismatched successive cancellation decoder