Non-Binary Polar Code Decoding with Stored Common Terms
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Solution Overview
Problem
The computational complexity of decoding non-binary polar codes increases exponentially with the number of input values, making efficient decoding challenging.
Innovation Solution
A low-complexity decoder is implemented using a lower triangular kernel to selectively calculate common terms for input symbols, reducing computational complexity by precomputing these terms and using them to determine output symbol values based on log likelihood ratios.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If non-binary polar codes with more input values are used, then correction capability and decoding throughput are improved, but computational complexity in decoding increases exponentially
Solution Approach 1:
The patent pre-calculates and stores common terms (log-likelihood ratios of input symbols) in a memory before the actual decoding process. By performing this preliminary computation and storage, the decoder avoids recalculating these terms during the main decoding operation, thereby reducing the exponential computational complexity while maintaining the correction capability of non-binary polar codes
Solution Approach 2:
The decoding process is segmented into distinct stages: generating log-likelihood ratios for input symbols, selectively calculating common terms for certain input symbols, storing these common terms in memory, and then using the stored common terms to determine output symbols. This segmentation allows the complex decoding task to be broken down into manageable parts with reduced computational burden
2Productivity
If non-binary polar codes with more input values are used, then decoding throughput is improved, but computational complexity in decoding increases exponentially
Solution Approach 1:
The patent performs preliminary calculation and storage of common terms in memory before the main decoding process. This pre-computation enables faster retrieval during decoding operations, thereby improving decoding throughput without requiring exponential computational resources during the actual decoding phase
Solution Approach 2:
The patent creates copies of common terms (log-likelihood ratios) and stores them in memory for repeated use. Instead of recalculating these terms for each decoding operation, the system uses the stored copies, which significantly reduces computational complexity while maintaining high decoding throughput
Data Source
AI summary
An apparatus that receives a non-binary polar code through a channel includes a low-complexity decoder and a memory. The low-complexity decoder is configured to selectively calculate first common terms for input symbols in the non-binary polar code other than a first input symbol corresponding to a first target output symbol. The selective calculation uses a lower triangular kernel and log likelihood ratios of the input symbols generated based on a channel characteristic of the channel. The low-complexity decoder is also configured to calculate log likelihood ratios of the first target output symbol using the first common terms and to determine a value of the first target output symbol based on the log likelihood ratios of the first target output symbol. The memory is accessible by the low-complexity decoder and is configured to store the first common terms.