Polar Code Windowed Decoding for Limited-Capacity Receivers
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Solution Overview
Problem
In communication systems where the transmitter and receiver have different computational capabilities, specifically when the receiver is less powerful than the transmitter, existing methods struggle to efficiently decode polar codewords of length N using a decoder capable of handling only polar codewords of length M<N, leading to increased block error rates.
Innovation Solution
The proposed solution involves applying a moving decoding window of length M to decode polar codewords of length N, utilizing a polar code based on windowed values and feedback from previously decoded sub-input vectors to improve decoding efficiency and reduce block error rates without increasing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a decoder with capacity M is used to decode polar codewords of length N (where M < N), then the decoder can operate within its computational limits, but the block error rate increases
Solution Approach 1:
The patent divides the polar codeword of length N into multiple segments of length M, allowing the decoder to process each segment separately. This segmentation enables the decoder to operate within its computational capacity while maintaining reliable decoding through systematic processing of divided code blocks
Solution Approach 2:
The patent transforms the decoding problem from a single-block dimension to a multi-block dimension by processing segmented codewords. This dimensional transformation allows the decoder to handle length-N codewords through multiple length-M processing steps, effectively resolving the capacity mismatch while preserving decoding reliability
2Productivity
If a moving decoding window of length M is applied to decode polar codewords of length N, then decoding efficiency is improved for asymmetric computational scenarios, but the complexity of the decoding process increases
Solution Approach 1:
The patent employs a moving decoding window that dynamically processes segments of the polar codeword. This dynamic approach allows the decoder to efficiently handle asymmetric computational scenarios by adaptively processing length-M segments from the length-N codeword, improving productivity while managing complexity through systematic window-based processing
Data Source
AI summary
A method and apparatus for generating a polar code; and also, encoding and decoding data using a polar code. The 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.