Decoding Polar Codes via Weighted-Window Soft Cancellation for Slowly-Varying Channel

Abstract: 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.