  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.
