Polar codes are a class of {bf structured} channel codes proposed by Ar{i}kan based on the principle of {bf channel polarization}, and can {bf achieve} the symmetric capacity of any Binary-input Discrete Memoryless Channel (B-DMC). The Soft CANcellation (SCAN) is a {bf low-complexity} {bf iterative} decoding algorithm of polar codes outperforming the widely-used Successive Cancellation (SC). Currently, in most cases, it is assumed that channel state is perfectly {bf known} at the decoder and remains {bf constant} during each codeword, which, however, is usually unrealistic. To decode polar codes for {bf slowly-varying} channel with {bf unknown} state, on the basis of SCAN, we propose the Weighted-Window SCAN (W$^2$SCAN). Initially, the decoder is seeded with a coarse estimate of channel state. Then after {bf each} SCAN iteration, the decoder progressively refines the estimate of channel state with the {bf quadratic programming}. The experimental results prove the significant superiority of W$^2$SCAN to SCAN and SC. In addition, a simple method is proposed to verify the correctness of SCAN decoding which requires neither Cyclic Redundancy Check (CRC) checksum nor Hash digest.
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