QC-LDPC Lifting Strategy for Flexible Code Length and Fewer Cycles
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Solution Overview
Problem
Existing quasi-cyclic low-density parity-check (QC-LDPC) codes face challenges in creating compact representations that support various lengths and rates, leading to issues like short cycles and poor weight spectra, which limit code gain and decoder throughput in wireless communication systems.
Innovation Solution
The method employs floor-scale modular lifting to generate optimal lifting values for circulants, allowing for flexible code lengths and circulant sizes, and uses a random matrix design approach to lift QC-LDPC codes directly from a mask matrix, avoiding catastrophic points and improving graph quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If traditional lifting methods are used for QC-LDPC codes, then code compactness is achieved, but short cycles appear in parity check matrices leading to lower code gain
Solution Approach 1:
The patent applies parameter changes by modifying the lifting value selection process. Instead of using fixed or simple sequential lifting values, the patent employs a pseudo-random number generator with specific seed values to generate optimized lifting values. This changes the parameter of lifting value selection from deterministic to pseudo-random, thereby avoiding short cycles while maintaining code compactness through the structured QC-LDPC format.
2Ease of manufacture
If sequential decoding methods are used, then implementation is simple, but decoder throughput is significantly limited
Solution Approach 1:
The patent applies dynamics by enabling parallel processing capabilities through the QC-LDPC code structure. The quasi-cyclic property with carefully selected lifting values allows the decoder to process multiple code bits simultaneously rather than sequentially. This dynamic parallel processing increases decoder throughput while maintaining implementation feasibility through the regular structure of QC-LDPC codes.
3Ease of manufacture
If fixed code length and rate are used, then encoding is straightforward, but flexibility to support various communication requirements is reduced
Solution Approach 1:
The patent applies universality by designing a QC-LDPC code system that can serve multiple code length and rate requirements through a single base matrix structure. By using variable lifting values generated from pseudo-random sequences, the same base matrix can be lifted to create codes with different lengths and rates, making the encoding system universally applicable to various communication requirements while maintaining the simplicity of QC-LDPC encoding.
Data Source
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AI summary
A method for quasi-cyclic low-density parity-check (QC-LDPC) encoding and decoding of a data packet by a lifted matrix is provided, the method comprising: lifting the QC-LDPC code for maximal code length Nmax and maximal circulant size Z upper of the base matrix; generating a plurality of optimal values r, for a plurality of circulants Z 1, Z 2,....,Z upper based on the QC-LDPC code lifted for maximal length Nmax, 0 ≤ r; ≤ Z upper - 1; saving the generated plurality of optimal values r; corresponding to the plurality of circulants Z,, Z 2,..., Z upper and a matrix for the QC-LDPC code lifted for maximal length N max in the memory unit; receiving a current circulant Z current from the plurality of circulants Z 1, Z 2,....,Z upper; selecting a current optimal value r current from the plurality of optimal values r; stored in the memory unit corresponding to the current circulant Z current; and lifting the base matrix based on the current optimal value r current, wherein a floor scale modular lifting of the base matrix is calculated as: where E(H upper ) is a value of circulant shift in the base matrix for maximal circulant size; wherein 0 ≤ r current ≤ z upper 1 and r current =1 is excluded. The apparatus for QC-LDPC encoding and decoding of a data packet by a lifted matrix is further provided.