Extended Polar Codes for Flexible Length and Reliable Storage
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Solution Overview
Problem
Conventional polar coding schemes restrict code length to powers of 2, leading to performance losses when code length is shortened, making them unsuitable for scenarios like data storage where code lengths are multiples of 8, resulting in severe errors.
Innovation Solution
The method involves generating an extended polar code by re-polarizing the least reliable information bit-channels using additional frozen bit-channels, allowing for adjustable code length and improved reliability by transforming input vectors into output vectors with enhanced error correction capabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional polar coding scheme is used with code length restricted to power of 2, then coding structure is simple, but code length cannot be adjusted to match data storage requirements (multiples of 8)
Solution Approach 1:
The code is segmented into two distinct parts: a standard polar code part with N bit-channels and an additional frozen part with q bit-channels. This segmentation allows the code to maintain the simple structure of standard polar codes while adding flexibility through the configurable additional frozen part, enabling code length adaptation to multiples of 8 without overwhelming complexity
Solution Approach 2:
The coding scheme becomes dynamic by allowing the additional frozen part to be selectively applied. The parameter q can be adjusted based on specific storage requirements, enabling the code length to adapt dynamically between N and N+q while maintaining a systematic structure that builds upon the standard polar code foundation
2Adaptability or versatility
If code length is shortened from power of 2 to match storage requirements, then code length flexibility is improved, but performance loss increases severely
Solution Approach 1:
Instead of uniformly shortening the entire code which degrades performance, the invention applies local quality by adding a targeted additional frozen part with q bit-channels. This localized extension allows the code to reach specific length requirements (multiples of 8) while preserving the high-reliability standard polar code part, thus maintaining overall coding performance
Solution Approach 2:
The additional frozen part is designed in advance with the understanding that it will be used to adjust code length to multiples of 8. By preparing this extensible structure beforehand, the system can seamlessly adapt to various storage requirements without experiencing the performance degradation associated with ad-hoc code shortening
3Adaptability or versatility
If additional frozen bit-channels are added to extend code length, then code length adaptability is improved, but code structure complexity increases
Solution Approach 1:
The additional frozen part serves multiple functions: it extends code length to match storage requirements, provides additional freezing capability for enhanced reliability, and maintains compatibility with standard polar code decoding. This multi-functionality justifies the added structural elements while delivering multiple benefits simultaneously
Data Source
AI summary
A method for increasing coding reliability includes generating a generator matrix for an extended polar code including a standard polar code part and an additional frozen part. The standard polar code part has N bit-channels, including K information bit-channels and N−K frozen bit-channels. The additional frozen part has q additional frozen bit-channels. Among the K information bit-channels, q information bit-channels are re-polarized using the q additional frozen bit-channels. The method further includes receiving an input vector including K information bits and N+q−K frozen bits, and transforming, using the generator matrix, the input vector to an output vector including N+q encoded bits. The K information bits are allocated to the K information bit-channels, and the N+q−K frozen bits are allocated to the N−K frozen bit-channels and the q additional frozen bit-channels.