Polar Code Sliding-Window Decoding for Subblock-Wise Encoding
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Solution Overview
Problem
Existing polar code decoding methods are inefficient due to their sequential nature and limited ability to handle finite code lengths, leading to incomplete polarization of bit-channels and reduced error correction performance.
Innovation Solution
The proposed method designs a polar code of length N that can be decoded using a sliding window of size M, where M < N, by employing a transformation matrix T and a frozen set F, allowing for iterative decoding of bit-channels within the sliding window.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If sequential Successive Cancellation decoding is used, then decoding is performed bit by bit with simple structure, but decoding efficiency is low and computational complexity is high for finite code lengths
Solution Approach 1:
The patent divides the polar code of length N into multiple subcodes of length M (where M < N) that can be independently decoded. This segmentation allows parallel processing of subcodes, improving decoding efficiency while keeping each subdecoder's structure simple and manageable.
Solution Approach 2:
The patent introduces a new dimension to the decoding process by using a sliding window approach that processes the codeword in overlapping segments. This transforms the single sequential decoding process into multiple parallel decoding operations across different window positions, significantly improving throughput.
2Reliability
If the code length N is used for complete polarization, then error correction performance is optimized, but computational complexity increases and receiver capabilities are exceeded
Solution Approach 1:
The patent applies partial action by decoding only a portion (M < N) of the polar code at each step rather than the complete code. Multiple partial decodings with sliding windows provide sufficient error correction performance for practical applications while dramatically reducing computational complexity compared to full-code decoding.
Solution Approach 2:
The patent changes the parameter of code length from N to M for the actual decoding operation. By using a smaller effective code length in each sliding window position, the computational complexity is reduced to match receiver capabilities while maintaining acceptable error correction performance through the overlapping window approach.
3Productivity
If sliding window decoding is applied, then decoding efficiency is improved and computational complexity is reduced, but complete polarization effect is lost
Solution Approach 1:
The patent merges the results from multiple sliding window decodings to reconstruct the complete decoded message. By combining the partial decoding results from different window positions, the system achieves both improved decoding efficiency through parallel processing and maintains the polarization effect's error correction benefits.
Solution Approach 2:
The sliding window approach ensures continuity of useful action by overlapping the decoding windows. This continuity allows the polarization effect to be applied repeatedly across different segments of the codeword, maintaining the beneficial error correction properties while enabling efficient parallel processing.
Data Source
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AI summary
The disclosure relates to generating a polar code and also to encoding and decoding data using a polar code. A method of generating a polar code includes obtaining a first matrix as an m-fold Kronecker product of a 2x2 binary lower triangular matrix where m = log2(M/2), M<N, and N is the length of a polar code to be generated. A second matrix may be obtained, where the inverse of the second matrix is a lower triangular band matrix. A transformation matrix may be generated for the polar code by calculating a Kronecker product of the second matrix with the first matrix. An information set I identifying reliable bit channels for the polar code may be determined. A polar codeword of length N may be obtained using the polar code that is decodable by iteratively applying a sliding decoding window of length M to the polar codeword, where M<N.