Network Coding Matrix Decomposition for Low-Power Decoding
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Solution Overview
Problem
Current network coding methods face challenges with high power consumption and complexity during the decoding process, leading to increased heat, battery drain, and memory usage, as well as elevated network complexity due to complex computations.
Innovation Solution
The method employs matrix decomposition to generate an encoding coefficient matrix through eigen-decomposition, using a random symmetric matrix to create a unitary matrix, diagonal matrix, and transposed matrix, which reduces computational complexity by converting data packets between real and Galois fields, and utilizing the transposed matrix for decoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional network coding decoding is performed, then data can be recovered from encoded packets, but power consumption and computational complexity increase significantly
Solution Approach 1:
The patent changes the parameter of the encoding coefficient matrix from a general invertible matrix to a unitary matrix. This parameter change transforms the decoding operation from complex matrix inversion to simple transposition, dramatically reducing computational complexity and power consumption while maintaining data recovery capability
Solution Approach 2:
The patent extracts and utilizes the specific property of unitary matrices (where the inverse equals the transpose) from linear algebra theory. By applying this mathematical property, the complex matrix inversion operation is replaced with a simpler transposition operation, reducing decoding complexity
2Reliability
If traditional network coding decoding is performed, then data can be recovered from encoded packets, but memory consumption increases due to complex computation requirements
Solution Approach 1:
By changing the matrix parameter to unitary structure, the patent reduces the computational operations needed for decoding. This parameter change directly reduces memory consumption by eliminating the need to store and process complex inversion calculations, while preserving the ability to recover original data
3Ease of manufacture
If complex matrix operations are used for network coding, then encoding can be performed, but overall network complexity increases
Solution Approach 1:
The patent applies parameter change by selecting unitary matrices as encoding coefficients. This choice simplifies the overall network complexity because the special structure of unitary matrices allows for efficient encoding and decoding operations, reducing the computational burden across the network while maintaining encoding capability
Solution Approach 2:
The unitary matrix structure serves multiple functions: it enables encoding operations, simplifies decoding to transposition, and reduces both computational and memory requirements. This multi-functionality reduces overall network complexity while maintaining full encoding and decoding capabilities
Data Source
AI summary
Provided are a network encoding method and apparatus, and a network decoding method and apparatus that performs network encoding and decoding through a transposed matrix of a unitary matrix decomposed from an encoding coefficient matrix by an eigen-decomposition. The network encoding method may include generating a random symmetric matrix indicating a binary square matrix, extracting an encoding coefficient matrix by decomposing the generated random symmetric matrix, generating encoding data by encoding source data using the extracted encoding coefficient matrix, forming a data packet including the generated encoding data and the encoding coefficient matrix, and converting the formed data packet from a real number field to a Galois field.