Self-Orthogonal QC Code Encoding for Higher Hamming Distance
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Solution Overview
Problem
Existing self-orthogonal quasi-cyclic (QC) codes face limitations in code word length and number of parity bits, making them restrictive for practical applications, and struggle to achieve a minimum hamming distance greater than w+1, especially when w>=3, which hinders the reduction of bit error rate (BER) and undetected error probability.
Innovation Solution
An encoding method for self-orthogonal QC codes is developed, where the parity check matrix is designed using circulant matrices with column weight w>=3 and minimum hamming distance w+2 or larger, by establishing specific relationships between elements of address sets in the circulant matrices to remove six-cycles and improve decoding performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If existing self-orthogonal QC codes are used, then the encoding structure is simple, but the minimum hamming distance is limited to w+1 and code word length is restricted
Solution Approach 1:
The patent changes the parameter of minimum hamming distance from the conventional w+1 to w+2 or larger by modifying the circulant matrix construction method. Specifically, it uses a different approach to define the address sets and permutation relationships in the circulant matrices, which directly increases the minimum distance while maintaining the self-orthogonal property and relatively simple encoding structure.
2Reliability
If code word length and number of parity bits are increased, then the error correction capability is improved, but the restrictiveness for practical applications increases
Solution Approach 1:
The patent creates a universal encoding method that can generate self-orthogonal QC codes with flexible code word lengths and parity bit numbers. By establishing a general construction method using circulant matrices with specific address set relationships, the invention enables the same encoding framework to adapt to different practical application requirements without losing its error correction capability or self-orthogonal property.
3Reliability
If minimum hamming distance is increased to w+2 or larger, then the bit error rate and undetected error probability are reduced, but the code design complexity increases
Solution Approach 1:
The patent achieves minimum hamming distance of w+2 or larger by changing the construction parameters of the circulant matrices. The key is to define address sets with specific permutation relationships that inherently guarantee the increased minimum distance. This parameter change is achieved through a systematic method that maintains design simplicity while improving error performance.
Data Source
AI summary
In an encoding and/or decoding method utilizing a self-orthogonal Quasi-Cyclic (QC) code whose parity check matrix is expressed by at least one circulant matrix, a code sequence is generated which satisfies a check matrix. The check matrix is designed so that a column weight w of each circulant matrix is three or larger and a minimum hamming distance of the code is w+2 or larger.