LDLC Matrix Construction Using Orthogonal Latin Squares
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Solution Overview
Problem
Communications systems, especially wireless ones, face significant challenges in recovering clean data from noisy signals due to prominent noise interference, which existing error correction schemes struggle to effectively mitigate, particularly in wireless or radio communications systems like WiMAX and Wi-Fi.
Innovation Solution
The implementation of a low-density lattice code (LDLC) matrix that is algebraically constructed and free from cycles of length less than six, utilizing Latin squares and incidence matrices to create a mapping matrix, combined with a sparse vector generator and random sign multiplier, enables efficient decoding of noisy data to recover clean data components.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional error correction schemes are used in wireless communications, then the system can operate with standard coding structures, but the noise interference cannot be effectively mitigated and error performance is poor
Solution Approach 1:
The patent changes the fundamental parameters of the coding structure by using algebraically constructed LDLC matrices with specific properties (no cycles of length less than six, derived from mutually orthogonal Latin squares). This transforms the coding approach from traditional concatenated codes to a novel algebraic construction that achieves near-Shannon theoretical capacity while maintaining systematic structure
Solution Approach 2:
The patent combines multiple mathematical structures (Latin squares, incidence matrices, algebraic constructions) to create a composite coding scheme. The LDLC matrix is constructed by combining these different mathematical components, creating a composite error correction structure that leverages the strengths of each component to achieve superior error performance
2Reliability
If algebraically constructed LDLC matrices without short cycles are used, then near-Shannon theoretical capacity is achieved with error performance within 0.5 dB at symbol error rate of 10^-6, but the matrix construction and decoding complexity increases
Solution Approach 1:
The patent performs preliminary action by pre-construction of LDLC matrices with guaranteed desirable properties (no short cycles, algebraic structure) before the actual communication process. These pre-constructed matrices are stored and reused, avoiding the need for complex real-time matrix construction during decoding operations
Solution Approach 2:
The patent segments the matrix construction process into distinct mathematical steps: generating mutually orthogonal Latin squares, constructing incidence matrices, and combining them to form the final LDLC matrix. This segmentation allows each step to be optimized independently and simplifies the overall construction process
Data Source
AI summary
According to one general aspect, a method including receiving noisy data via a communications channel, wherein the noisy data includes a clean data component and a noise component. In various embodiments, the method may also include decoding, utilizing a low-density lattice code (LDLC) matrix, the received noisy data to substantially recover the clean data component. In some embodiments, the LDLC matrix may not include a matrix of less than a length of six cycles. In one embodiment, the LDLC matrix may be algebraically constructed. In various embodiments, the method may include storing the decoded clean data component.