Polar Code Decoding with Coupled Subcodes for Lower ML Complexity
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Solution Overview
Problem
The high complexity of Maximum Likelihood (ML) decoding for Polar codes in communications systems leads to inefficient decoding processes, particularly due to the exponential complexity of O(2^K), which hinders effective data transmission reliability.
Innovation Solution
The proposed method divides the Polar code into coupled subcodes and employs a two-stage or three-stage parallel decoding process, calculating independent and combined squared Euclidean distances to reduce decoding complexity and improve throughput.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Maximum Likelihood decoding is applied to Polar codes, then decoding reliability is improved, but decoding complexity increases exponentially to O(2^K)
Solution Approach 1:
The Polar code of length N is divided into m coupled subcodes of length N/m (where N and m are integer powers of 2 and N > m). Each subcode is decoded independently in parallel, reducing the exponential complexity from O(2^N) to O(m * 2^(N/m)), while maintaining decoding reliability through subsequent combined processing.
2Measurement precision
If traditional ML decoding is used for Polar codes, then accurate decoding is achieved, but decoding throughput is reduced due to high computational complexity
Solution Approach 1:
The decoding process is segmented into multiple stages: first dividing the Polar code into m subcodes and decoding them independently in parallel to obtain preliminary results, then performing combined processing on these results. This segmentation enables higher throughput by utilizing parallel computation while maintaining accuracy through the final combination stage that ensures optimal decoding decisions.
Solution Approach 2:
The method performs preliminary independent decoding on each subcode before performing the final combined processing. This preliminary action on subcodes provides initial decoding results that guide the subsequent combined processing, reducing the search space and computational burden while maintaining decoding accuracy.
3Reliability
If complete ML decoding is performed on the entire Polar code, then optimal decoding results are obtained, but decoding delay increases due to processing the entire code at once
Solution Approach 1:
The Polar code is segmented into m subcodes that are decoded independently and in parallel. This segmentation reduces decoding delay by enabling simultaneous processing of multiple subcodes, while the subsequent combined processing stage ensures that the final decoding results maintain optimality by considering the relationships between subcodes.
Data Source
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AI summary
A Polar code decoding method is provided, including: receiving a to-be-decoded Polar code having a length of N, and dividing the to-be-decoded Polar code into m subcodes of the Polar code that are coupled to each other, where each subcode of the Polar code has a length of N/m, N and m are integer powers of 2, and N > m; calculating squared Euclidean distances of input bits that are independent of each other in the m subcodes of the Polar code, to obtain minimum squared Euclidean distances of the input bits that are independent of each other in the m subcodes of the Polar code, where the minimum squared Euclidean distances of the input bits that are independent of each other in the m subcodes of the Polar code are referred to as independent minimum squared Euclidean distances; obtaining, according to the m independent minimum squared Euclidean distances, a minimum squared Euclidean distance of input bits that are coupled to each other in the m subcodes of the Polar code, where the minimum squared Euclidean distance of the input bits that are coupled to each other in the m subcodes of the Polar code is referred to as a combined minimum squared Euclidean distance; and obtaining input bits that are in the m subcodes of the Polar code and that meet the independent minimum squared Euclidean distances and the combined minimum squared Euclidean distance, and obtaining a decoding result of the to-be-decoded Polar code with reference to relationships between the m subcodes of the Polar code and the to-be-decoded Polar code.