Polar Code Sliding-Window Decoding Under Receiver Size Limits
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Solution Overview
Problem
In communication systems where the receiver has less computational capability than the transmitter, existing methods for decoding polar codes of length N using a receiver capable of handling only polar codewords of length M<N result in increased block error rates due to independent transmissions, as correct decoding requires all codewords to be decoded correctly, and any error leads to overall decoding failure.
Innovation Solution
The proposed method employs a moving decoding window of length M to decode polar codewords by using a polar code based on windowed values, where the already decoded sub-input vector is fed back to obtain channel likelihoods for subsequent sub-input vector decoding, improving block error rate performance without increasing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If independent transmissions are used to decode polar codes of length N using a receiver capable of handling only polar codewords of length M<N, then the receiver can operate within its computational capability, but the block error rate increases because correct decoding requires all codewords to be decoded correctly
Solution Approach 1:
The polar code of length N is divided into S=N/M segments, each of length M. Instead of transmitting the entire code as one block, the segmentation allows the receiver to process multiple smaller codewords independently, adapting to its computational limitations while maintaining the ability to recover the original data through combining results from multiple segments
Solution Approach 2:
The patent implements feedback mechanisms where decoding results from previously processed segments are fed back into the decoding process for subsequent segments. This feedback allows the receiver to utilize information from correctly decoded segments to improve the decoding of remaining segments, thereby reducing the overall block error rate despite the segmented approach
2Reliability
If a full-length classical polar code of length N is decoded, then optimal block error rate performance is achieved, but the computational complexity increases beyond the capability of the receiver
Solution Approach 1:
The full-length polar code decoding problem is segmented into multiple smaller sub-problems of length M. Each segment can be decoded independently using the receiver's limited computational resources, avoiding the need to perform computationally intensive full-length N decoding while still achieving near-optimal performance through the combination of segment results
Solution Approach 2:
Instead of performing complete full-length decoding, the receiver performs partial decoding on segments of length M. This partial action is sufficient to achieve the desired performance level while staying within computational constraints, effectively doing 'enough but not too much' computation
Data Source
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 2×2 binary lower triangular matrix where m=log 2(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.