Protograph Quasi-Cyclic Polar Codes for Low-Latency Decoding
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Solution Overview
Problem
Conventional polar codes suffer from poor performance and long latency due to short cycles in their factor graphs, which hinder parallelizable decoding and increase computational complexity, making them unsuitable for latency-critical systems.
Innovation Solution
The introduction of protograph lifting expansion for polar coding, which eliminates short cycles through hill-climbing optimization of frozen bits allocation and protograph permutation, enabling highly parallelizable decoding and reducing computational complexity by using quasi-cyclic permutations and irregular pruning of proto-polarization units.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional polar codes are used, then encoding and decoding can be performed, but short cycles in factor graphs cause poor performance and long latency
Solution Approach 1:
The polar code is segmented into multiple proto-polarization units arranged in a protograph structure. This segmentation allows the code to eliminate short cycles while maintaining the polarization property, thereby improving error correction performance and reducing decoding latency through parallelizable decoding.
Solution Approach 2:
The invention transitions from the traditional factor graph representation to a protograph representation with lifting expansion. This dimensional change introduces a new structure where proto-polarization units are arranged in a multi-stage protograph, eliminating short cycles and enabling parallelizable decoding.
2Reliability
If conventional polar codes are used, then decoding can be performed, but computational complexity increases due to short cycles
Solution Approach 1:
By segmenting the polar code into proto-polarization units in a protograph structure, the invention eliminates short cycles that cause high computational complexity. The segmented structure enables more efficient decoding algorithms while maintaining error correction performance.
Solution Approach 2:
The invention changes the structural parameters of the polar code by introducing a protograph lifting expansion with multiple stages and proto-polarization units. This parameter change transforms the code structure to eliminate short cycles, thereby reducing computational complexity while preserving reliability.
3Productivity
If protograph lifting expansion is introduced to eliminate short cycles, then parallelizable decoding is enabled, but code structure becomes more complex
Solution Approach 1:
The protograph structure with lifting expansion serves multiple functions: it eliminates short cycles, enables parallelizable decoding, and maintains the polarization property. This universal structure achieves multiple goals simultaneously, improving productivity without excessive complexity increase.
Solution Approach 2:
The invention uses copying by replicating proto-polarization units across multiple stages in the protograph. This copying approach enables parallelizable decoding while maintaining a systematic structure that is manageable and implementable, balancing productivity improvement with structural complexity.
4Reliability
If longer polar codes are used to improve performance, then coding gain increases, but decoding latency increases
Solution Approach 1:
The invention segments the coding function into multiple proto-polarization units that can be processed in parallel. This segmentation allows achieving the performance of longer codes through parallel processing of shorter code segments, thereby increasing coding gain without proportionally increasing decoding latency.
Solution Approach 2:
The multi-stage protograph structure implements periodic action by repeating proto-polarization units across stages. This periodic structure enables parallelizable decoding that achieves the coding gain of longer codes while maintaining low latency through simultaneous processing of multiple stages.
Data Source
AI summary
Data communications and storage systems require error control techniques to be transferred successfully without failure. Polar coding has been used as a state-of-the-art forward error correction code for such an error control technique. However, the conventional decoding based on successive cancellation has a drawback in its poor performance and long latency to complete. Because the factor graph of polar codes has a lot of short cycles, a parallelizable belief propagation decoding also does not perform well. The method and system of the present invention provide a way to resolve the issues by introducing a protograph lifting expansion for a polar coding family so that highly parallelizable decoding is realized to achieve a high coding gain and high throughput without increasing the computational complexity and latency. The invention enables an iterative message passing to work properly by eliminating short cycles through a hill-climbing optimization of frozen bits allocation and permutation.