Polar Code Construction With Overlapping Sub-Channel Allocation
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Solution Overview
Problem
Polar codes used in 5G wireless communications face challenges in achieving optimal error correction performance due to limitations in code length and decoding complexity, particularly in finite code lengths and varying channel conditions, which affect the allocation of sub-channels for information and frozen bits.
Innovation Solution
The method involves selecting sub-channels for information bits from overlapping constituent polar codes of length Nref < N, using a chained polar coding approach that optimizes bit allocation and polarization, allowing for dynamic bit distribution across multiple sub-codes to enhance coding gain and reduce decoding complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional polar codes of length N are used, then channel capacity is approached, but decoding complexity increases and error correction performance is limited in finite code lengths
Solution Approach 1:
The patent divides a polar code of length N into multiple constituent polar codes of shorter length Nref. Each constituent code processes a subset of sub-channels independently, reducing the decoding complexity from O(N) to O(Nref) while maintaining error correction performance through the overlapping structure that ensures all sub-channels are covered.
Solution Approach 2:
The patent employs a hierarchical structure where multiple shorter constituent polar codes (Nref) are nested within the overall code framework of length N. The constituent codes overlap and share common sub-channels, creating a nested arrangement that achieves long-code performance with short-code decoding complexity.
2Reliability
If code length N is increased to approach channel capacity, then coding gain improves, but computational complexity increases
Solution Approach 1:
The patent segments the computational task of decoding a length-N code into multiple independent decoding tasks of length-Nref. This segmentation maintains the coding gain benefits of long codes by covering all N sub-channels through overlapping constituent codes, while reducing computational complexity to match the smaller Nref length.
Solution Approach 2:
The patent uses multiple constituent codes that overlap and cover the same sub-channels multiple times. This excessive action ensures that all sub-channels are adequately covered to achieve full coding gain, while each individual constituent code operates at lower computational complexity Nref.
3Reliability
If sub-channel allocation is optimized for maximum capacity, then error correction performance improves, but allocation complexity increases
Solution Approach 1:
The patent divides sub-channel allocation into multiple independent allocation processes, one for each constituent polar code of length Nref. Each constituent code allocates its subset of sub-channels independently using simplified criteria, avoiding the complexity of optimizing the entire N-length code while achieving near-optimal performance through the overlapping structure.
Data Source
AI summary
A sub-channel to carry an information bit, in input bits that are to be encoded, is selected from each of multiple subsets of sub-channels that are provided by a length N polar code. The subsets include sub-channels that are associated with respective overlapping constituent polar codes of the length N polar code. The constituent polar codes are of length Nref<N. An ordered sequence of length Nref, instead of a longer ordered sequence of length N, may be used in selecting the sub-channels. The input bits are encoded to generate a codeword, and the codeword is transmitted.